{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T22:33:21Z","timestamp":1777761201958,"version":"3.51.4"},"reference-count":265,"publisher":"Emerald","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,5,30]]},"abstract":"<jats:p>In distributed data storage, information pertaining to a given data file is stored across multiple storage units or nodes in redundant fashion to protect against the principal concern, namely, the possibility of data loss arising from the failure of individual nodes. The simplest form of such protection is replication. The explosive growth in the amount of data generated on a daily basis brought up a second major concern, namely minimization of the overhead associated with such redundant storage. This concern led to the adoption by the storage industry of erasure-recovery codes such as Reed-Solomon (RS) codes and more generally, maximum distance separable codes, as these codes offer the lowest-possible storage overhead for a given level of reliability.<\/jats:p>\n                  <jats:p>In the setting of a large data center, where the amount of stored data can run into several exabytes, a third concern arises, namely the need for efficient recovery from a commonplace occurrence, the failure of a single storage unit. One measure of efficiency in node repair is how small one can make the amount of data download needed to repair a failed unit, termed the repair bandwidth. This was the subject of the seminal paper by Dimakis et al. [50] in which an entirely new class of codes called regenerating codes was introduced, that within a certain repair framework, had the minimum-possible repair bandwidth. A second measure relates to the number of helper nodes contacted for node repair, termed the repair degree. A low repair degree is desirable as this means that a smaller number of nodes are impacted by the failure of a given node. The landmark paper by Gopalan et al. [72] focuses on this second measure, leading to the development of the theory of locally recoverable codes. The two events also led to the creation of a third class of codes known as locally regenerating codes, where the aim is to simultaneously achieve reduced repair bandwidth and low repair degree. Research in a different direction led researchers to take a fresh look at the challenge of efficient RS-code repair, and led to the identification of improved repair schemes for RS codes that have significantly reduced repair bandwidth.<\/jats:p>\n                  <jats:p>This monograph introduces the reader to these different approaches towards efficient node repair and presents many of the fundamental bounds and code constructions that have since emerged. Several open problems are identified, and many of the sections have a notes subsection at the end that provides additional background.<\/jats:p>","DOI":"10.1561\/0100000115","type":"journal-article","created":{"date-parts":[[2022,5,30]],"date-time":"2022-05-30T04:05:17Z","timestamp":1653883517000},"page":"547-813","source":"Crossref","is-referenced-by-count":33,"title":["Codes for Distributed Storage"],"prefix":"10.1108","volume":"19","author":[{"given":"Vinayak","family":"Ramkumar","sequence":"first","affiliation":[{"name":"Indian Institute of Science , Bengaluru,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. B.","family":"Balaji","sequence":"additional","affiliation":[{"name":"Qualcomm , Bengaluru,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Birenjith","family":"Sasidharan","sequence":"additional","affiliation":[{"name":"Govt. Engineering College , Barton Hill, Trivandrum,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Myna","family":"Vajha","sequence":"additional","affiliation":[{"name":"Qualcomm , Bengaluru,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Nikhil","family":"Krishnan","sequence":"additional","affiliation":[{"name":"International Institute of Information Technology Bangalore ,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. Vijay","family":"Kumar","sequence":"additional","affiliation":[{"name":"Indian Institute of Science , Bengaluru,","place":["India"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2022,5,30]]},"reference":[{"issue":"5","key":"2026032712182334900_ref001","doi-asserted-by":"crossref","first-page":"3481","DOI":"10.1109\/TIT.2018.2800042","article-title":"Combinatorial alphabet-dependent bounds for locally recoverable codes","volume":"64","author":"Agarwal","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref002","first-page":"1","article-title":"An alternate construction of an access-optimal regenerating code with optimal sub-packetization level","volume-title":"Proc. Twenty First National Conference on Communications","author":"Agarwal"},{"issue":"4","key":"2026032712182334900_ref003","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1109\/18.850663","article-title":"Network information flow","volume":"46","author":"Ahlswede","year":"2000","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref004","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1109\/TIT.2017.2780230","article-title":"When can intelligent helper node selection improve the performance of distributed storage networks?","volume":"64","author":"Ahmad","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1-2","key":"2026032712182334900_ref005","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1017\/S0963548398003411","article-title":"Combinatorial Nullstellensatz","volume":"8","author":"Alon","year":"1999","journal-title":"Combinatorics, Probability and Computing"},{"key":"2026032712182334900_ref006","first-page":"979","article-title":"An exponential lower bound on the sub-packetization of MSR codes","volume-title":"Proc. 51st Annual ACM SIGACT Symposium on Theory of Computing","author":"Alrabiah"},{"key":"2026032712182334900_ref007","doi-asserted-by":"crossref","DOI":"10.1109\/TIT.2021.3112286","article-title":"An exponential lower bound on the sub-packetization of minimum storage regenerating codes","author":"Alrabiah","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref008","article-title":"Erasure codes for distributed storage: Tight bounds and matching constructions","volume":"abs\/1806.04474","author":"Babu","year":"2018","journal-title":"CoRR"},{"key":"2026032712182334900_ref009","article-title":"On lower bounds on sub-packetization level of MSR codes and on the structure of optimal-access MSR codes achieving the bound","volume":"abs\/1710.05876v3","author":"Babu","year":"2021","journal-title":"CoRR"},{"issue":"10","key":"2026032712182334900_ref010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11432-018-9482-6","article-title":"Erasure coding for distributed storage: An overview","volume":"61","author":"Balaji","year":"2018","journal-title":"Science China Information Sciences"},{"key":"2026032712182334900_ref011","first-page":"2381","article-title":"A tight lower bound on the sub-packetization level of optimal-access MSR and MDS codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Balaji"},{"key":"2026032712182334900_ref012","first-page":"655","article-title":"Binary codes with locality for multiple erasures having short block length","volume-title":"Proc. IEEE International Symposium on Information Theory, ISIT 2016","author":"Balaji"},{"issue":"2","key":"2026032712182334900_ref013","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1109\/TIT.2019.2958970","article-title":"A tight rate bound and matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures","volume":"66","author":"Balaji","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref014","first-page":"3155","article-title":"Bounds on the rate and minimum distance of codes with availability","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Balaji"},{"key":"2026032712182334900_ref015","first-page":"1881","article-title":"On partial maximally-recoverable and maximally-recoverable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Balaji"},{"issue":"3","key":"2026032712182334900_ref016","doi-asserted-by":"crossref","first-page":"733","DOI":"10.4171\/jems\/316","article-title":"On sets of vectors of a finite vector space in which every subset of basis size is a basis","volume":"14","author":"Ball","year":"2012","journal-title":"Journal of the European Mathematical Society"},{"issue":"1","key":"2026032712182334900_ref017","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10623-012-9658-6","article-title":"On sets of vectors of a finite vector space in which every subset of basis size is a basis II","volume":"65","author":"Ball","year":"2012","journal-title":"Designs, Codes and Cryptography"},{"issue":"10","key":"2026032712182334900_ref018","doi-asserted-by":"crossref","first-page":"6056","DOI":"10.1109\/TIT.2019.2919830","article-title":"Codes with hierarchical locality from covering maps of curves","volume":"65","author":"Ballentine","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref019","doi-asserted-by":"crossref","first-page":"4928","DOI":"10.1109\/TIT.2017.2700859","article-title":"Locally recoverable codes on algebraic curves","volume":"63","author":"Barg","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref020","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/s10623-022-01020-8","article-title":"A construction of maximally recoverable codes","volume":"90","author":"Barg","year":"2022","journal-title":"Designs, Codes and Cryptography"},{"key":"2026032712182334900_ref021","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-3-319-63931-4_4","volume-title":"Algebraic Geometry for Coding Theory and Cryptography","author":"Barg","year":"2017"},{"key":"2026032712182334900_ref022","first-page":"1","article-title":"Unequal locality and recovery for locally recoverable codes with availability","volume-title":"Twenty-third National Conference on Communications","author":"Bhadane"},{"key":"2026032712182334900_ref023","first-page":"1855","volume-title":"Handbook of Coding Theory","author":"Blaum","year":"1998"},{"key":"2026032712182334900_ref024","article-title":"Construction of PMDS and SD codes extending RAID 5","volume":"abs\/1305.0032","author":"Blaum","year":"2013","journal-title":"CoRR"},{"issue":"2","key":"2026032712182334900_ref025","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/12.364531","article-title":"EVENODD: An efficient scheme for tolerating double disk failures in RAID architectures","volume":"44","author":"Blaum","year":"1995","journal-title":"IEEE Transactions on computers"},{"issue":"2","key":"2026032712182334900_ref026","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/18.485722","article-title":"MDS array codes with independent parity symbols","volume":"42","author":"Blaum","year":"1996","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"2026032712182334900_ref027","doi-asserted-by":"crossref","first-page":"4510","DOI":"10.1109\/TIT.2013.2252395","article-title":"Partial-MDS codes and their application to RAID type of architectures","volume":"59","author":"Blaum","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref028","doi-asserted-by":"crossref","first-page":"2673","DOI":"10.1109\/TIT.2016.2536720","article-title":"Construction of partial MDS and sector-disk codes with two global parity symbols","volume":"62","author":"Blaum","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref029","doi-asserted-by":"crossref","first-page":"2946","DOI":"10.1137\/20M1356658","article-title":"Constructing partial MDS codes from reducible algebraic curves","volume":"35","author":"Bogart","year":"2021","journal-title":"SIAM J. Discret. Math."},{"issue":"11","key":"2026032712182334900_ref030","doi-asserted-by":"crossref","first-page":"5787","DOI":"10.1109\/TIT.2015.2477406","article-title":"Bounds on the size of locally recoverable codes","volume":"61","author":"Cadambe","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref031","doi-asserted-by":"crossref","first-page":"2974","DOI":"10.1109\/TIT.2013.2237752","article-title":"Asymptotic interference alignment for optimal repair of MDS codes in distributed storage","volume":"59","author":"Cadambe","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref032","first-page":"1225","article-title":"Permutation code: Optimal exact-repair of a single failed node in MDS code based distributed storage systems","volume-title":"Porc. IEEE International Symposium on Information Theory Proceedings, ISIT 2011","author":"Cadambe"},{"key":"2026032712182334900_ref033","first-page":"1850","article-title":"Polynomial length MDS codes with optimal repair in distributed storage","volume-title":"Proc. Forty Fifth Asilomar Conference on Signals, Systems and Computers","author":"Cadambe"},{"issue":"8","key":"2026032712182334900_ref034","doi-asserted-by":"crossref","first-page":"4853","DOI":"10.1109\/TIT.2020.2977647","article-title":"On optimal locally repairable codes with super-linear length","volume":"66","author":"Cai","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref035","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1109\/TIT.2021.3120016","article-title":"A construction of maximally recoverable codes with order-optimal field size","volume":"68","author":"Cai","year":"2022","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref036","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1109\/LCOMM.2016.2627569","article-title":"A general construction for PMDS codes","volume":"21","author":"Calis","year":"2017","journal-title":"IEEE Communications Letters"},{"key":"2026032712182334900_ref037","unstructured":"Ceph V14.1.0 Nautilus\n           (Release Candidate 1), url: url: https:\/\/docs.ceph.com\/en\/nautilus\/releases\/nautilus\/."},{"issue":"4","key":"2026032712182334900_ref038","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.1109\/TIT.2017.2761120","article-title":"Constructions of optimal cyclic (r,\u03b4) locally repairable codes","volume":"64","author":"Chen","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref039","first-page":"1876","article-title":"Sector-disk codes and partial MDS codes with up to three global parities","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Chen"},{"key":"2026032712182334900_ref040","first-page":"486","article-title":"On the maximally recoverable property for multi-protection group codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Chen"},{"issue":"2","key":"2026032712182334900_ref041","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/TIT.2019.2941744","article-title":"Explicit constructions of MSR codes for clustered distributed storage: The rack-aware storage model","volume":"66","author":"Chen","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref042","first-page":"616","article-title":"Cyclic LRC codes with hierarchy and availability","volume-title":"IEEE International Symposium on Information Theory","author":"Chen"},{"issue":"12","key":"2026032712182334900_ref043","doi-asserted-by":"crossref","first-page":"7439","DOI":"10.1109\/TIT.2020.3017666","article-title":"Enabling optimal access and error correction for the repair of Reed\u2013Solomon codes","volume":"66","author":"Chen","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref044","doi-asserted-by":"crossref","first-page":"5051","DOI":"10.1109\/TIT.2021.3071447","article-title":"Improved schemes for asymptotically optimal repair of MDS codes","volume":"67","author":"Chowdhury","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref045","first-page":"1","article-title":"Row-diagonal parity for double disk failure correction","volume-title":"Proc. 3rd USENIX Conference on File and Storage Technologies","author":"Corbett"},{"issue":"1","key":"2026032712182334900_ref046","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1145\/2447712.2447735","article-title":"An overview of codes tailor-made for better repairability in networked distributed storage systems","volume":"44","author":"Datta","year":"2013","journal-title":"SIGACT News"},{"issue":"10","key":"2026032712182334900_ref047","doi-asserted-by":"crossref","first-page":"6567","DOI":"10.1109\/TIT.2018.2827942","article-title":"Repairing Reed-Solomon codes with multiple erasures","volume":"64","author":"Dau","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref048","first-page":"346","article-title":"Optimal repair schemes for some families of full-length Reed-Solomon codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Dau"},{"issue":"3","key":"2026032712182334900_ref049","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/0097-3165(78)90015-8","article-title":"Bilinear forms over a finite field, with applications to coding theory","volume":"25","author":"Delsarte","year":"1978","journal-title":"J. Comb. Theory, Ser. A"},{"issue":"9","key":"2026032712182334900_ref050","doi-asserted-by":"crossref","first-page":"4539","DOI":"10.1109\/TIT.2010.2054295","article-title":"Network coding for distributed storage systems","volume":"56","author":"Dimakis","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref051","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1109\/JPROC.2010.2096170","article-title":"A survey on network codes for distributed storage","volume":"99","author":"Dimakis","year":"2011","journal-title":"Proceedings of the IEEE"},{"key":"2026032712182334900_ref052","first-page":"89","article-title":"Hierarchical codes: How to make erasure codes attractive for peer-to-peer storage systems","volume-title":"Proc. P2P\u201908, Eighth International Conference on Peer-to-Peer Computing","author":"Duminuco"},{"issue":"1","key":"2026032712182334900_ref053","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/s12083-009-0044-8","article-title":"Hierarchical codes: A flexible trade-off for erasure codes in peer-to-peer storage systems","volume":"3","author":"Duminuco","year":"2010","journal-title":"Peer-to-Peer Netw. Appl."},{"issue":"3","key":"2026032712182334900_ref054","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1137\/20M1346742","article-title":"Multilinear algebra for distributed storage","volume":"5","author":"Duursma","year":"2021","journal-title":"SIAM Journal on Applied Algebra and Geometry"},{"key":"2026032712182334900_ref055","first-page":"1","article-title":"Multilinear algebra for minimum storage regenerating codes: A generalization of the productmatrix construction","author":"Duursma","year":"2021","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"issue":"2","key":"2026032712182334900_ref056","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1109\/TIT.2018.2840995","article-title":"Shortened regenerating codes","volume":"65","author":"Duursma","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref057","article-title":"Outer bounds for exact repair codes","volume":"abs\/1406.4852","author":"Duursma","year":"2014","journal-title":"CoRR"},{"key":"2026032712182334900_ref058","first-page":"1","article-title":"Low bandwidth repair of the RS(10, 4) Reed-Solomon code","volume-title":"Proc. Information Theory and Applications Workshop","author":"Duursma"},{"key":"2026032712182334900_ref059","first-page":"1510","article-title":"Fractional repetition codes for repair in distributed storage systems","volume-title":"Proc. 48th Annual Allerton Conference on Communication, Control, and Computing","author":"El Rouayheb"},{"key":"2026032712182334900_ref060","first-page":"2061","article-title":"Linear exact repair rate region of (k + 1, k, k) distributed storage systems: A new approach","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Elyasi"},{"issue":"12","key":"2026032712182334900_ref061","doi-asserted-by":"crossref","first-page":"6683","DOI":"10.1109\/TIT.2016.2616137","article-title":"Determinant coding: A novel framework for exact-repair regenerating codes","volume":"62","author":"Elyasi","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref062","first-page":"1241","article-title":"A cascade code construction for (n, k, d) distributed storage systems","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Elyasi"},{"issue":"9","key":"2026032712182334900_ref063","doi-asserted-by":"crossref","first-page":"5469","DOI":"10.1109\/TIT.2019.2904294","article-title":"Determinant codes with helperindependent repair for single and multiple failures","volume":"65","author":"Elyasi","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"2026032712182334900_ref064","doi-asserted-by":"crossref","first-page":"7490","DOI":"10.1109\/TIT.2020.3033338","article-title":"Cascade codes for distributed storage systems","volume":"66","author":"Elyasi","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref065","first-page":"887","article-title":"Repair-optimal MDS array codes over GF(2)","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"En Gad"},{"key":"2026032712182334900_ref066","first-page":"1","article-title":"Constructions of optimal and almost optimal locally repairable codes","volume-title":"Proc. 4th International Conference on Wireless Communications, Vehicular Technology, Information Theory and Aerospace Electronic Systems","author":"Ernvall"},{"key":"2026032712182334900_ref067","article-title":"The existence of fractional repetition codes","volume":"abs\/1201.3547","author":"Ernvall","year":"2012","journal-title":"CoRR"},{"key":"2026032712182334900_ref068","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.disc.2014.01.016","article-title":"On the locality of codeword symbols in non-linear codes","volume":"324","author":"Forbes","year":"2014","journal-title":"Discrete Math."},{"issue":"1","key":"2026032712182334900_ref069","first-page":"3","article-title":"Theory of codes with maximum rank distance","volume":"21","author":"Gabidulin","year":"1985","journal-title":"Problemy Peredachi Informatsii"},{"issue":"6","key":"2026032712182334900_ref070","doi-asserted-by":"crossref","first-page":"3692","DOI":"10.1109\/TIT.2018.2890201","article-title":"Constructions of partial MDS codes over small fields","volume":"65","author":"Gabrys","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"2026032712182334900_ref071","doi-asserted-by":"crossref","first-page":"5245","DOI":"10.1109\/TIT.2014.2332338","article-title":"Explicit maximally recoverable codes with locality","volume":"60","author":"Gopalan","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"2026032712182334900_ref072","doi-asserted-by":"crossref","first-page":"6925","DOI":"10.1109\/TIT.2012.2208937","article-title":"On the locality of codeword symbols","volume":"58","author":"Gopalan","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref073","first-page":"2092","article-title":"Maximally recoverable codes for grid-like topologies","volume-title":"Proc. Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"Gopalan"},{"key":"2026032712182334900_ref074","first-page":"676","article-title":"Binary cyclic codes that are locally repairable","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Goparaju"},{"key":"2026032712182334900_ref075","first-page":"1","article-title":"Data secrecy in distributed storage systems under exact repair","volume-title":"Proc. International Symposium on Network Coding","author":"Goparaju"},{"issue":"10","key":"2026032712182334900_ref076","doi-asserted-by":"crossref","first-page":"6318","DOI":"10.1109\/TIT.2017.2690662","article-title":"Minimum storage regenerating codes for all parameters","volume":"63","author":"Goparaju","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref077","doi-asserted-by":"crossref","first-page":"2770","DOI":"10.1109\/TIT.2014.2309000","article-title":"An improved subpacketization bound for minimum storage regenerating codes","volume":"60","author":"Goparaju","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref078","first-page":"25","article-title":"Improved maximally recoverable LRCs using skew polynomials","author":"Gopi","year":"2021","journal-title":"Electron. Colloquium Comput. Complex."},{"issue":"10","key":"2026032712182334900_ref079","doi-asserted-by":"crossref","first-page":"6066","DOI":"10.1109\/TIT.2020.2990981","article-title":"Maximally recoverable LRCs: A field size lower bound and constructions for few heavy parities","volume":"66","author":"Gopi","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref080","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1109\/LCOMM.2019.2921540","article-title":"Uniform minors in maximally recoverable codes","volume":"23","author":"Grezet","year":"2019","journal-title":"IEEE Communications Letters"},{"key":"2026032712182334900_ref081","article-title":"On weak dress codes for cloud storage","volume":"abs\/1302.3681","author":"Gupta","year":"2013","journal-title":"CoRR"},{"key":"2026032712182334900_ref082","first-page":"1077","article-title":"Near-optimal repair of Reed-Solomon codes with low sub-packetization","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Guruswami"},{"issue":"10","key":"2026032712182334900_ref083","doi-asserted-by":"crossref","first-page":"6133","DOI":"10.1109\/TIT.2020.2988459","article-title":"Constructions of maximally recoverable local reconstruction codes via function fields","volume":"66","author":"Guruswami","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref084","first-page":"2109","article-title":"MDS code constructions with small sub-packetization and near-optimal repair bandwidth","volume-title":"Proc. Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"Guruswami"},{"issue":"9","key":"2026032712182334900_ref085","first-page":"5684","article-title":"Repairing Reed-Solomon codes","volume":"63","author":"Guruswami","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"2026032712182334900_ref086","doi-asserted-by":"crossref","first-page":"3662","DOI":"10.1109\/TIT.2019.2891765","article-title":"How long can optimal locally repairable codes be?","volume":"65","author":"Guruswami","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref087","first-page":"2531","article-title":"Reliable memories with subline accesses","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Han"},{"key":"2026032712182334900_ref088","first-page":"440","article-title":"Some results on optimal locally repairable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Hao"},{"key":"2026032712182334900_ref089","first-page":"171","article-title":"On optimal ternary locally repairable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Hao"},{"key":"2026032712182334900_ref090","doi-asserted-by":"crossref","DOI":"10.1109\/ISIT.2018.8437466","article-title":"On the maximal code length of optimal linear locally repairable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Hao"},{"key":"2026032712182334900_ref091","first-page":"1","article-title":"On the linear codes with (r, \u03b4) locality for distributed storage","volume-title":"Proc. IEEE International Conference on Communications, ICC 2017","author":"Hao"},{"issue":"12","key":"2026032712182334900_ref092","doi-asserted-by":"crossref","first-page":"7465","DOI":"10.1109\/TIT.2020.3021707","article-title":"Bounds and constructions of locally repairable codes: Parity-check matrix approach","volume":"66","author":"Hao","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"2026032712182334900_ref093","doi-asserted-by":"crossref","first-page":"317","DOI":"10.3934\/amc.2018020","article-title":"Locally recoverable codes with availability (t\u22652) from fiber products of curves","volume":"12","author":"Haymaker","year":"2018","journal-title":"Adv. Math. Commun."},{"issue":"2","key":"2026032712182334900_ref094","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1109\/18.370144","article-title":"Bounds on the minimum support weights","volume":"41","author":"Helleseth","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref095","doi-asserted-by":"crossref","first-page":"4730","DOI":"10.1109\/TIT.2019.2902835","article-title":"Rack-aware regenerating codes for data centers","volume":"65","author":"Hou","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref096","first-page":"1591","article-title":"New constructions of SD and MR codes over small finite fields","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Hu"},{"key":"2026032712182334900_ref097","first-page":"1","article-title":"Broadcast repair for wireless distributed storage systems","volume-title":"Proc. 10th International Conference on Information, Communications and Signal Processing","author":"Hu"},{"key":"2026032712182334900_ref098","first-page":"21","article-title":"NCCloud: Applying network coding for the storage repair in a cloud-of-clouds","volume-title":"Proc. 10th USENIX conference on File and Storage Technologies","author":"Hu"},{"key":"2026032712182334900_ref099","first-page":"245","article-title":"Double regenerating codes for hierarchical data centers","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Hu"},{"issue":"2","key":"2026032712182334900_ref100","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1109\/JSAC.2010.100216","article-title":"Cooperative recovery of distributed storage systems from multiple losses with network coding","volume":"28","author":"Hu","year":"2010","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2026032712182334900_ref101","article-title":"Erasure Coding in Windows Azure Storage","volume-title":"talk presented at the SNIA Storage Developer Conference","author":"Huang"},{"key":"2026032712182334900_ref102","first-page":"79","article-title":"Pyramid codes: Flexible schemes to trade space for access efficiency in reliable data storage systems","volume-title":"Proc. 6th IEEE Int. Symposium on Network Computing and Applications","author":"Huang"},{"key":"2026032712182334900_ref103","first-page":"15","article-title":"Erasure coding in windows azure storage","volume-title":"Proc. 2012 USENIX Annual Technical Conference","author":"Huang"},{"issue":"1","key":"2026032712182334900_ref104","doi-asserted-by":"crossref","first-page":"3:1","DOI":"10.1145\/2435204.2435207","article-title":"Pyramid codes: Flexible schemes to trade space for access efficiency in reliable data storage systems","volume":"9","author":"Huang","year":"2013","journal-title":"ACM Trans. Storage"},{"issue":"3","key":"2026032712182334900_ref105","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1109\/TIT.2016.2647601","article-title":"On secrecy capacity of minimum storage regenerating codes","volume":"63","author":"Huang","year":"2017","journal-title":"IEEE Trans. on Inf. Theory"},{"issue":"11","key":"2026032712182334900_ref106","doi-asserted-by":"crossref","first-page":"6218","DOI":"10.1109\/TIT.2016.2608949","article-title":"Security concerns in minimum storage cooperative regenerating codes","volume":"62","author":"Huang","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"2026032712182334900_ref107","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1109\/TIT.2018.2880239","article-title":"Improved upper bounds on systematic-length for linear minimum storage regenerating codes","volume":"65","author":"Huang","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref108","first-page":"1","article-title":"Cyclic linear binary locally repairable codes","volume-title":"Proc. IEEE Information Theory Workshop","author":"Huang"},{"issue":"11","key":"2026032712182334900_ref109","doi-asserted-by":"crossref","first-page":"6268","DOI":"10.1109\/TIT.2016.2605119","article-title":"Binary linear locally repairable codes","volume":"62","author":"Huang","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref110","unstructured":"Information theory inequality prover\n          , url: http:\/\/user-www.ie.cuhk.edu.hk\/~ITIP\/."},{"issue":"1","key":"2026032712182334900_ref111","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/TIT.2019.2946627","article-title":"Constructions of locally repairable codes with multiple recovering sets via rational function fields","volume":"66","author":"Jin","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref112","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/TIT.2019.2946637","article-title":"Construction of optimal locally repairable codes via automorphism groups of rational function fields","volume":"66","author":"Jin","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref113","first-page":"1028","article-title":"Security for minimum storage regenerating codes and locally repairable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Kadhe"},{"key":"2026032712182334900_ref114","article-title":"Rate optimal binary linear locally repairable codes with small availability","volume":"abs\/1701.02456","author":"Kadhe","year":"2017","journal-title":"CoRR"},{"key":"2026032712182334900_ref115","first-page":"166","article-title":"Rate optimal binary linear locally repairable codes with small availability","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Kadhe"},{"key":"2026032712182334900_ref116","first-page":"504","article-title":"Explicit MBR all-symbol locality codes","volume-title":"Proc. IEEE International Symposium on Information Theory, Istanbul, Turkey","author":"Kamath"},{"issue":"8","key":"2026032712182334900_ref117","doi-asserted-by":"crossref","first-page":"4637","DOI":"10.1109\/TIT.2014.2329872","article-title":"Codes with local regeneration and erasure correction","volume":"60","author":"Kamath","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref118","first-page":"1","article-title":"Repairing multiple failures with coordinated and adaptive regenerating codes","volume-title":"Proc. International Symposium on Networking Coding","author":"Kermarrec"},{"issue":"2","key":"2026032712182334900_ref119","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/LCOMM.2017.2776141","article-title":"New constructions of binary and ternary locally repairable codes using cyclic codes","volume":"22","author":"Kim","year":"2018","journal-title":"IEEE Communications Letters"},{"key":"2026032712182334900_ref120","first-page":"211","article-title":"Secure determinant codes: A class of secure exact-repair regenerating codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Kleckler","year":"2019"},{"key":"2026032712182334900_ref121","first-page":"652","article-title":"Secure determinant codes: Type-II security","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Kleckler","year":"2020"},{"issue":"5","key":"2026032712182334900_ref122","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1109\/TNET.2003.818197","article-title":"An algebraic approach to network coding","volume":"11","author":"Koetter","year":"2003","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"2026032712182334900_ref123","article-title":"Optimal LRC codes for all lenghts n &lt;= q","volume":"abs\/1802.00157","author":"Kolosov","year":"2018","journal-title":"CoRR"},{"issue":"2","key":"2026032712182334900_ref124","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3381832","article-title":"On fault tolerance, locality, and optimality in locally repairable codes","volume":"16","author":"Kolosov","year":"2020","journal-title":"ACM Transactions on Storage"},{"key":"2026032712182334900_ref125","first-page":"1366","article-title":"Scalable constructions of fractional repetition codes in distributed storage systems","volume-title":"Proc. 49th Annual Allerton Conference on Communication, Control, and Computing","author":"Koo"},{"issue":"9","key":"2026032712182334900_ref126","doi-asserted-by":"crossref","first-page":"5228","DOI":"10.1109\/TIT.2014.2319271","article-title":"Secure cooperative regenerating codes for distributed storage systems","volume":"60","author":"Koyluoglu","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"2026032712182334900_ref127","first-page":"1281","article-title":"General subpacketized access-optimal regenerating codes","volume":"20","author":"Kralevska","year":"2016","journal-title":"IEEE Communications Letters"},{"key":"2026032712182334900_ref128","article-title":"HashTag erasure codes: From theory to practice","author":"Kralevska","year":"2017","journal-title":"IEEE Transactions on Big Data"},{"key":"2026032712182334900_ref129","first-page":"1196","article-title":"Codes with combined locality and regeneration having optimal rate, dmin and linear field size","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Krishnan"},{"key":"2026032712182334900_ref130","article-title":"Evaluation of codes with inherent double replication for Hadoop","volume-title":"Proc. 6th USENIX Workshop on Hot Topics in Storage and File Systems","author":"Krishnan"},{"issue":"6","key":"2026032712182334900_ref131","doi-asserted-by":"crossref","first-page":"2346","DOI":"10.1109\/TCOMM.2018.2797988","article-title":"Exploiting locality for improved decoding of binary cyclic codes","volume":"66","author":"Krishnan","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"2026032712182334900_ref132","first-page":"71","article-title":"On MBR codes with replication","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Krishnan"},{"issue":"7","key":"2026032712182334900_ref133","doi-asserted-by":"crossref","first-page":"4156","DOI":"10.1109\/TIT.2019.2897705","article-title":"New bounds and generalizations of locally recoverable codes with availability","volume":"65","author":"Kruglik","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref134","article-title":"Codes with local regeneration","volume-title":"talk presented at the conference on Trends in Coding Theory","author":"Kumar"},{"key":"2026032712182334900_ref135","first-page":"835","article-title":"Weight enumerators and higher support weights of maximally recoverable codes","volume-title":"Proc. 53rd Annual Allerton Conference on Communication, Control, and Computing","author":"Lalitha"},{"issue":"3","key":"2026032712182334900_ref136","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/TST.2013.6522585","article-title":"Erasure coding for cloud storage systems: A survey","volume":"18","author":"Li","year":"2013","journal-title":"Tsinghua Science and Technology"},{"key":"2026032712182334900_ref137","first-page":"1623","article-title":"A generic transformation for optimal repair bandwidth and rebuilding access in MDS codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Li"},{"issue":"4","key":"2026032712182334900_ref138","doi-asserted-by":"crossref","first-page":"2162","DOI":"10.1109\/TIT.2020.3036386","article-title":"A systematic construction of MDS codes with small sub-packetization level and near-optimal repair bandwidth","volume":"67","author":"Li","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref139","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1109\/TPDS.2016.2623309","article-title":"Beehive: Erasure codes for fixing multiple failures in distributed storage systems","volume":"28","author":"Li","year":"2017","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"2026032712182334900_ref140","first-page":"942","article-title":"A tradeoff between the subpacketization size and the repair bandwidth for Reed-Solomon code","volume-title":"Proc. 55th Annual Allerton Conference on Communication, Control, and Computing","author":"Li"},{"issue":"11","key":"2026032712182334900_ref141","doi-asserted-by":"crossref","first-page":"7087","DOI":"10.1109\/TIT.2019.2923609","article-title":"Construction of asymptotically good locally repairable codes via automorphism groups of function fields","volume":"65","author":"Li","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref142","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1109\/TIT.2018.2844216","article-title":"Optimal locally repairable codes via elliptic curves","volume":"65","author":"Li","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"2026032712182334900_ref143","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1109\/TIT.2014.2378255","article-title":"A unified form of exact-MSR codes via product-matrix frameworks","volume":"61","author":"Lin","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"12","key":"2026032712182334900_ref144","doi-asserted-by":"crossref","first-page":"3232","DOI":"10.1109\/TPDS.2013.2297109","article-title":"Novel repair-by-transfer codes and systematic exact-MBR codes with lower complexities and smaller field sizes","volume":"25","author":"Lin","year":"2014","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"2026032712182334900_ref145","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/978-3-319-70293-3_14","article-title":"An overview of coding for distributed storage systems","author":"Liu","year":"2018","journal-title":"Network Coding and Subspace Designs"},{"key":"2026032712182334900_ref146","first-page":"2440","article-title":"On storage codes allowing partially collaborative repairs","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Liu"},{"key":"2026032712182334900_ref147","article-title":"Maximally recoverable local reconstruction codes from subspace direct sum systems","volume":"abs\/2111.03244","author":"Liu","year":"2021","journal-title":"CoRR"},{"issue":"10","key":"2026032712182334900_ref148","first-page":"4405","article-title":"Explicit constructions of high-rate MSR codes with optimal access property over small finite fields","volume":"66","author":"Liu","year":"2018","journal-title":"IEEE Trans. Communications"},{"key":"2026032712182334900_ref149","unstructured":"Locally repairable erasure code plugin\n          , url: http:\/\/docs.ceph.com\/docs\/master\/rados\/operations\/erasure-code-lrc\/."},{"issue":"9","key":"2026032712182334900_ref150","doi-asserted-by":"crossref","first-page":"5711","DOI":"10.1109\/TIT.2021.3052488","article-title":"Repair rate lower bounds for distributed storage","volume":"67","author":"Luby","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref151","doi-asserted-by":"crossref","first-page":"2:1","DOI":"10.1145\/3281276","article-title":"Liquid cloud storage","volume":"15","author":"Luby","year":"2019","journal-title":"ACM Trans. Storage"},{"key":"2026032712182334900_ref152","article-title":"Distributed storage algorithms with optimal tradeoffs","volume":"abs\/2101.05223","author":"Luby","year":"2021","journal-title":"CoRR"},{"issue":"8","key":"2026032712182334900_ref153","doi-asserted-by":"crossref","first-page":"4987","DOI":"10.1109\/TCOMM.2021.3083320","article-title":"Constructions of optimal binary locally recoverable codes via a general construction of linear codes","volume":"69","author":"Luo","year":"2021","journal-title":"IEEE Transactions on Communications"},{"issue":"2","key":"2026032712182334900_ref154","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1109\/TIT.2018.2854717","article-title":"Optimal locally repairable codes of distance 3 and 4 via cyclic codes","volume":"65","author":"Luo","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref155","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1137\/19M1248443","article-title":"Optimal binary linear locally repairable codes with disjoint repair groups","volume":"33","author":"Ma","year":"2019","journal-title":"SIAM J. Discret. Math."},{"key":"2026032712182334900_ref156","volume-title":"The theory of error-correcting codes","author":"MacWilliams","year":"1977"},{"issue":"5","key":"2026032712182334900_ref157","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1109\/TIT.2018.2876542","article-title":"Repairing multiple failures for scalar MDS codes","volume":"65","author":"Mardia","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref158","article-title":"A general family of MSRD codes and PMDS codes with smaller field sizes from extended Moore matrices","volume":"abs\/2011.14109","author":"Mart\u00ednez-Pe\u00f1as","year":"2020","journal-title":"CoRR"},{"issue":"12","key":"2026032712182334900_ref159","doi-asserted-by":"crossref","first-page":"7790","DOI":"10.1109\/TIT.2019.2924888","article-title":"Universal and dynamic locally repairable codes with maximal recoverability via sum-rank codes","volume":"65","author":"Mart\u00ednez-Pe\u00f1as","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref160","first-page":"1","article-title":"On minimum distance of locally repairable codes","volume-title":"Proc. 15th Canadian Workshop on Information Theory","author":"Mehrabi"},{"key":"2026032712182334900_ref161","unstructured":"Microsoft research blog: A better way to store data\n          , url: https:\/\/www.microsoft.com\/en-us\/research\/blog\/better-way-storedata\/."},{"key":"2026032712182334900_ref162","first-page":"2056","article-title":"New bounds on the (n, k, d) storage systems with exact repair","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Mohajer"},{"issue":"8","key":"2026032712182334900_ref163","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1109\/LCOMM.2017.2697424","article-title":"Binary locally repairable codes with minimum distance at least six based on partial t-spreads","volume":"21","author":"Nam","year":"2017","journal-title":"IEEE Communications Letters"},{"key":"2026032712182334900_ref164","first-page":"1215","article-title":"Self-repairing homomorphic codes for distributed storage systems","volume-title":"Proc. IEEE INFOCOM","author":"Oggier"},{"issue":"4","key":"2026032712182334900_ref165","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1109\/TIT.2016.2531720","article-title":"Fractional repetition codes with flexible repair from combinatorial designs","volume":"62","author":"Olmez","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref166","first-page":"81","article-title":"Opening the chrysalis: On the real repair performance of MSR codes","volume-title":"Proc. 14th USENIX Conference on File and Storage Technologies","author":"Pamies-Juarez"},{"issue":"5","key":"2026032712182334900_ref167","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.1109\/TIT.2013.2241819","article-title":"Repair optimal erasure codes through Hadamard designs","volume":"59","author":"Papailiopoulos","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"2026032712182334900_ref168","doi-asserted-by":"crossref","first-page":"5843","DOI":"10.1109\/TIT.2014.2325570","article-title":"Locally repairable codes","volume":"60","author":"Papailiopoulos","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"2026032712182334900_ref169","doi-asserted-by":"crossref","first-page":"6734","DOI":"10.1109\/TIT.2011.2162191","article-title":"Securing dynamic distributed storage systems against eavesdropping and adversarial attacks","volume":"57","author":"Pawar","year":"2011","journal-title":"IEEE Trans. on Inf. Theory"},{"key":"2026032712182334900_ref170","first-page":"2338","article-title":"DRESS Codes for the storage cloud: Simple randomized constructions","volume-title":"Proc. IEEE International Symposium on Information Theory Proceedings","author":"Pawar"},{"issue":"8","key":"2026032712182334900_ref171","doi-asserted-by":"crossref","first-page":"5783","DOI":"10.1109\/TIT.2018.2806342","article-title":"The storage versus repair-bandwidth trade-off for clustered storage systems","volume":"64","author":"Prakash","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref172","first-page":"2776","article-title":"Optimal linear codes with a local-error-correction property","volume-title":"Proc. IEEE International Symposium on Information Theory Proceedings","author":"Prakash"},{"key":"2026032712182334900_ref173","first-page":"859","article-title":"The storage-repair-bandwidth trade-off of exact repair linear regenerating codes for the case d=k=n-1","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Prakash"},{"issue":"12","key":"2026032712182334900_ref174","doi-asserted-by":"crossref","first-page":"7771","DOI":"10.1109\/TIT.2019.2934124","article-title":"Codes with locality for two erasures","volume":"65","author":"Prakash","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref175","first-page":"1962","article-title":"Codes with locality for two erasures","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Prakash"},{"issue":"3","key":"2026032712182334900_ref176","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s00200-020-00430-2","article-title":"Optimal RS-like LRC codes of arbitrary length","volume":"31","author":"Rajput","year":"2020","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"key":"2026032712182334900_ref177","first-page":"1","article-title":"Achieving secrecy capacity of minimum storage regenerating codes for all feasible (n, k, d) parameter values","volume-title":"National Conference on Communications","author":"Rameshwar"},{"key":"2026032712182334900_ref178","first-page":"735","volume-title":"Concise Encyclopedia of Coding Theory","author":"Ramkumar","year":"2021"},{"key":"2026032712182334900_ref179","first-page":"1243","article-title":"Explicit construction of optimal exact regenerating codes for distributed storage","volume-title":"Proc. 47th Annu. Allerton Conf. Communication, Control, and Computing","author":"Rashmi"},{"key":"2026032712182334900_ref180","first-page":"81","article-title":"Having your cake and eating it too: Jointly optimal erasure codes for I\/O, storage, and network-bandwidth","volume-title":"Proc. 13th USENIX Conference on File and Storage Technologies","author":"Rashmi"},{"key":"2026032712182334900_ref181","first-page":"1202","article-title":"Regenerating codes for errors and erasures in distributed storage","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Rashmi"},{"issue":"3","key":"2026032712182334900_ref182","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1109\/TIT.2017.2769101","article-title":"Information-theoretically secure erasure codes for distributed storage","volume":"64","author":"Rashmi","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref183","first-page":"331","article-title":"A \"Hitchhiker\u2019s\" guide to fast and efficient data reconstruction in erasure-coded data centers","volume-title":"Proc. ACM SIGCOMM Conference","author":"Rashmi"},{"issue":"9","key":"2026032712182334900_ref184","first-page":"5802","article-title":"A piggybacking design framework for read-and download-efficient distributed storage codes","volume":"63","author":"Rashmi","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref185","doi-asserted-by":"crossref","first-page":"5227","DOI":"10.1109\/TIT.2011.2159049","article-title":"Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction","volume":"57","author":"Rashmi","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref186","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1109\/TIT.2017.2658660","article-title":"Constructions of high-rate minimum storage regenerating codes over small fields","volume":"63","author":"Raviv","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref187","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1109\/TIT.2013.2288784","article-title":"Optimal locally repairable and secure codes for distributed storage systems","volume":"60","author":"Rawat","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref188","first-page":"1406","article-title":"Secrecy capacity of minimum storage regenerating codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Rawat"},{"issue":"1","key":"2026032712182334900_ref189","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1109\/TIT.2013.2288784","article-title":"Optimal locally repairable and secure codes for distributed storage systems","volume":"60","author":"Rawat","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref190","first-page":"1","article-title":"Progress on high-rate MSR codes: Enabling arbitrary number of helper nodes","volume-title":"Proc. Information Theory and Applications Workshop","author":"Rawat"},{"issue":"12","key":"2026032712182334900_ref191","doi-asserted-by":"crossref","first-page":"7529","DOI":"10.1109\/TIT.2018.2871451","article-title":"Centralized repair of multiple node failures with applications to communication efficient secret sharing","volume":"64","author":"Rawat","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref192","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13634-015-0292-0","article-title":"Cooperative local repair in distributed storage","volume":"2015","author":"Rawat","year":"2015","journal-title":"EURASIP Journal on Advances in Signal Processing"},{"issue":"8","key":"2026032712182334900_ref193","doi-asserted-by":"crossref","first-page":"4481","DOI":"10.1109\/TIT.2016.2524510","article-title":"Locality and availability in distributed storage","volume":"62","author":"Rawat","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref194","first-page":"2043","article-title":"\u03f5-MSR codes with small sub-packetization","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Rawat"},{"issue":"10","key":"2026032712182334900_ref195","doi-asserted-by":"crossref","first-page":"6506","DOI":"10.1109\/TIT.2018.2810095","article-title":"MDS code constructions with small sub-packetization and near-optimal repair bandwidth","volume":"64","author":"Rawat","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"2026032712182334900_ref196","first-page":"300","article-title":"Polynomial codes over certain finite fields","volume":"8","author":"Reed","year":"1960","journal-title":"Journal of the SIAM"},{"issue":"9","key":"2026032712182334900_ref197","doi-asserted-by":"crossref","first-page":"5765","DOI":"10.1109\/TIT.2021.3090939","article-title":"Locally recoverable codes on surfaces","volume":"67","author":"Salgado","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref198","first-page":"2430","article-title":"An improved outer bound on the storage-repair-bandwidth tradeoff of exact-repair regenerating codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Sasidharan"},{"key":"2026032712182334900_ref199","first-page":"1257","article-title":"Codes with hierarchical locality","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Sasidharan"},{"key":"2026032712182334900_ref200","first-page":"2051","article-title":"A high-rate MSR code with polynomial sub-packetization level","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Sasidharan"},{"key":"2026032712182334900_ref201","article-title":"Codes with hierarchical locality","volume":"abs\/1501.06683","author":"Sasidharan","year":"2015","journal-title":"CoRR"},{"key":"2026032712182334900_ref202","first-page":"1611","article-title":"High-rate regenerating codes through layering","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Sasidharan"},{"issue":"4","key":"2026032712182334900_ref203","first-page":"255","article-title":"Outer bounds on the storage-repair bandwidth trade-off of exact-repair regenerating codes","volume":"3","author":"Sasidharan","year":"2016","journal-title":"Int. Journal Inf. Coding Theory"},{"key":"2026032712182334900_ref204","first-page":"2048","article-title":"An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d &lt; (n-1)","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Sasidharan"},{"key":"2026032712182334900_ref205","article-title":"An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and all-node repair","volume":"abs\/1607.07335","author":"Sasidharan","year":"2016","journal-title":"CoRR"},{"key":"2026032712182334900_ref206","article-title":"An explicit, coupled-layer construction of a high-rate regenerating code with low sub-packetization level, small field size and d &lt; (n-1)","volume":"abs\/1701.07447","author":"Sasidharan","year":"2022","journal-title":"CoRR"},{"issue":"5","key":"2026032712182334900_ref207","first-page":"325","article-title":"XORing elephants: Novel erasure codes for big data","volume":"6","author":"Sathiamoorthy","year":"2013","journal-title":"PVLDB"},{"issue":"66","key":"2026032712182334900_ref208","doi-asserted-by":"crossref","first-page":"73","DOI":"10.2307\/2001955","article-title":"On the inversion of certain matrices","volume":"13","author":"Schechter","year":"1959","journal-title":"Mathematical Tables and Other Aids to Computation"},{"issue":"1","key":"2026032712182334900_ref209","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/BF02410779","article-title":"Curve razionali normali ek-archi negli spazi finiti","volume":"39","author":"Segre","year":"1955","journal-title":"Annali di Matematica Pura ed Applicata"},{"key":"2026032712182334900_ref210","first-page":"1","article-title":"Improved layered regenerating codes characterizing the exact-repair storage-repair bandwidth tradeoff for certain parameter sets","volume-title":"Proc. IEEE Information Theory Workshop","author":"Senthoor"},{"issue":"3","key":"2026032712182334900_ref211","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1109\/TIT.2011.2173792","article-title":"Distributed storage codes with repair-by-transfer and non-achievability of interior points on the storage-bandwidth tradeoff","volume":"58","author":"Shah","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref212","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.1109\/TIT.2011.2178588","article-title":"Interference alignment in regenerating codes for distributed storage: Necessity and code constructions","volume":"58","author":"Shah","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref213","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1109\/LCOMM.2013.040213.130006","article-title":"On minimizing data-read and download for storage-node recovery","volume":"17","author":"Shah","year":"2013","journal-title":"IEEE Communications Letters"},{"issue":"8","key":"2026032712182334900_ref214","doi-asserted-by":"crossref","first-page":"3182","DOI":"10.1109\/TCOMM.2016.2581163","article-title":"A class of binary locally repairable codes","volume":"64","author":"Shahabinejad","year":"2016","journal-title":"IEEE Transactions on Communications"},{"issue":"5","key":"2026032712182334900_ref215","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/JSAC.2014.140519","article-title":"A Repair framework for scalar MDS codes","volume":"32","author":"Shanmugam","year":"2014","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"11","key":"2026032712182334900_ref216","doi-asserted-by":"crossref","first-page":"7253","DOI":"10.1109\/TIT.2017.2750156","article-title":"On the tradeoff region of secure exact-repair regenerating codes","volume":"63","author":"Shao","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref217","first-page":"1","article-title":"On maximally recoverable codes for product topologies","volume-title":"Proc. Twenty Fourth National Conference on Communications","author":"Shivakrishna"},{"issue":"11","key":"2026032712182334900_ref218","doi-asserted-by":"crossref","first-page":"7229","DOI":"10.1109\/TIT.2013.2274265","article-title":"Cooperative regenerating codes","volume":"59","author":"Shum","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref219","first-page":"1247","article-title":"Optimal binary locally repairable codes via anticodes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Silberstein"},{"key":"2026032712182334900_ref220","doi-asserted-by":"crossref","DOI":"10.1109\/ISIT.2013.6620541","article-title":"Optimal locally repairable codes via rank-metric codes","volume-title":"conference on Trends in Coding Theory","author":"Silberstein"},{"issue":"8","key":"2026032712182334900_ref221","doi-asserted-by":"crossref","first-page":"4164","DOI":"10.1109\/TIT.2015.2442231","article-title":"Optimal fractional repetition codes based on graphs and designs","volume":"61","author":"Silberstein","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref222","doi-asserted-by":"crossref","DOI":"10.1007\/s10623-017-0358-0","article-title":"Anticode-based locally repairable codes with high availability","volume":"86","author":"Silberstein","year":"2018","journal-title":"Designs, Codes and Cryptography"},{"issue":"2","key":"2026032712182334900_ref223","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TIT.1964.1053661","article-title":"Maximum distance q-nary codes","volume":"10","author":"Singleton","year":"1964","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"2026032712182334900_ref224","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/TIT.2018.2837860","article-title":"Capacity of clustered distributed storage","volume":"65","author":"Sohn","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref225","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1109\/JSAC.2014.140521","article-title":"Optimal locally repairable linear codes","volume":"32","author":"Song","year":"2014","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"5","key":"2026032712182334900_ref226","doi-asserted-by":"crossref","first-page":"3513","DOI":"10.1109\/TIT.2017.2711611","article-title":"On sequential locally repairable codes","volume":"64","author":"Song","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref227","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TIT.2011.2105003","article-title":"Exact-repair MDS code construction using interference alignment","volume":"57","author":"Suh","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"2026032712182334900_ref228","doi-asserted-by":"crossref","first-page":"4661","DOI":"10.1109\/TIT.2014.2321280","article-title":"A family of optimal locally recoverable codes","volume":"60","author":"Tamo","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref229","doi-asserted-by":"crossref","first-page":"1597","DOI":"10.1109\/TIT.2012.2227110","article-title":"Zigzag codes: MDS array codes with optimal rebuilding","volume":"59","author":"Tamo","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"2026032712182334900_ref230","doi-asserted-by":"crossref","first-page":"3070","DOI":"10.1109\/TIT.2016.2518663","article-title":"Bounds on the parameters of locally recoverable codes","volume":"62","author":"Tamo","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref231","first-page":"345","article-title":"Cyclic LRC codes, binary LRC codes, and upper bounds on the distance of cyclic codes","volume":"3","author":"Tamo","year":"2016","journal-title":"Int. J. Inf. Coding Theory"},{"issue":"12","key":"2026032712182334900_ref232","doi-asserted-by":"crossref","first-page":"6661","DOI":"10.1109\/TIT.2016.2555813","article-title":"Optimal locally repairable codes and connections to matroid theory","volume":"62","author":"Tamo","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref233","doi-asserted-by":"crossref","first-page":"2028","DOI":"10.1109\/TIT.2014.2305698","article-title":"Access versus bandwidth in codes for storage","volume":"60","author":"Tamo","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref234","doi-asserted-by":"crossref","first-page":"2673","DOI":"10.1109\/TIT.2018.2884075","article-title":"The repair problem for Reed\u2013Solomon codes: Optimal repair of single and multiple erasures with almost optimal node size","volume":"65","author":"Tamo","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"2026032712182334900_ref235","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1109\/TIT.2016.2544340","article-title":"Toward optimal secure distributed storage systems with exact repair","volume":"62","author":"Tandon","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"4","key":"2026032712182334900_ref236","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1109\/TIT.2015.2408595","article-title":"Layered exact-repair regenerating codes via embedded error correction and block designs","volume":"61","author":"Tian","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"2026032712182334900_ref237","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1109\/JSAC.2014.140516","article-title":"Characterizing the rate region of the (4, 3, 3) exact-repair regenerating codes","volume":"32","author":"Tian","year":"2014","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"2026032712182334900_ref238","article-title":"A note on the rate region of exact-repair regenerating codes","volume":"abs\/1503.00011","author":"Tian","year":"2015","journal-title":"CoRR"},{"key":"2026032712182334900_ref239","first-page":"2376","article-title":"Explicit MSR codes with optimal access, optimal sub-packetization and small field size for d = k+1, k+2, k+3","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Vajha"},{"key":"2026032712182334900_ref240","first-page":"139","article-title":"Clay codes: Moulding MDS codes to yield an MSR Code","volume-title":"Proc. 16th USENIX Conference on File and Storage Technologies","author":"Vajha"},{"issue":"11","key":"2026032712182334900_ref241","doi-asserted-by":"crossref","first-page":"6979","DOI":"10.1109\/TIT.2014.2351404","article-title":"Repair locality with multiple erasure tolerance","volume":"60","author":"Wang","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"2026032712182334900_ref242","doi-asserted-by":"crossref","first-page":"5280","DOI":"10.1109\/TIT.2015.2472515","article-title":"An integer programming-based bound for locally repairable codes","volume":"61","author":"Wang","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref243","first-page":"2033","article-title":"Bounds and constructions for linear locally repairable codes over binary fields","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Wang"},{"key":"2026032712182334900_ref244","first-page":"400","article-title":"Exact cooperative regenerating codes with minimum-repair-bandwidth for distributed storage","volume-title":"Proc. IEEE INFOCOM","author":"Wang"},{"key":"2026032712182334900_ref245","first-page":"445","article-title":"Two classes of (r, t)-locally repairable codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Wang"},{"key":"2026032712182334900_ref246","first-page":"1866","article-title":"Achieving arbitrary locality and availability in binary codes","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Wang"},{"key":"2026032712182334900_ref247","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1142\/S0129054120500112","article-title":"Constructions of (r,t)-LRC based on totally isotropic subspaces in symplectic space over finite fields","volume":"31","author":"Wang","year":"2020","journal-title":"International Journal of Foundations of Computer Science"},{"key":"2026032712182334900_ref248","first-page":"1374","article-title":"On codes for optimal rebuilding access","volume-title":"Proc. 49th Annual Allerton Conference on Communication, Control, and Computing 2011","author":"Wang"},{"key":"2026032712182334900_ref249","first-page":"1182","article-title":"Long MDS codes for optimal repair bandwidth","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Wang"},{"issue":"5","key":"2026032712182334900_ref250","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1109\/18.133259","article-title":"Generalized Hamming weights for linear codes","volume":"37","author":"Wei","year":"1991","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"2026032712182334900_ref251","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1109\/JSAC.2010.100217","article-title":"Existence and construction of capacity-achieving network codes for distributed storage","volume":"28","author":"Wu","year":"2010","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"1","key":"2026032712182334900_ref252","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/TIT.2019.2940975","article-title":"Locally repairable codes: Joint sequential\u2013parallel repair for multiple node failures","volume":"66","author":"Yavari","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"2026032712182334900_ref253","doi-asserted-by":"crossref","first-page":"7038","DOI":"10.1109\/TIT.2017.2740939","article-title":"The rate region for secure distributed storage systems","volume":"63","author":"Ye","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref254","first-page":"1202","article-title":"Explicit constructions of MDS array codes and RS codes with optimal repair bandwidth","volume-title":"Proc. IEEE International Symposium on Information Theory","author":"Ye"},{"issue":"4","key":"2026032712182334900_ref255","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1109\/TIT.2017.2661313","article-title":"Explicit constructions of high-rate MDS array codes with optimal repair bandwidth","volume":"63","author":"Ye","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"2026032712182334900_ref256","doi-asserted-by":"crossref","first-page":"6307","DOI":"10.1109\/TIT.2017.2730863","article-title":"Explicit constructions of optimal-access MDS codes with nearly optimal sub-packetization","volume":"63","author":"Ye","year":"2017","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"2026032712182334900_ref257","doi-asserted-by":"crossref","first-page":"1639","DOI":"10.1109\/TIT.2018.2856206","article-title":"Cooperative repair: Constructions of optimal MDS codes for all admissible parameters","volume":"65","author":"Ye","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"2026032712182334900_ref258","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1109\/18.641556","article-title":"A framework for linear information inequalities","volume":"43","author":"Yeung","year":"1997","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref259","first-page":"1","article-title":"Optimal linear and cyclic locally repairable codes over small fields","volume-title":"Proc. IEEE Information Theory Workshop","author":"Zeh"},{"issue":"12","key":"2026032712182334900_ref260","doi-asserted-by":"crossref","first-page":"7333","DOI":"10.1109\/TIT.2020.2977636","article-title":"Constructions of optimal codes with hierarchical locality","volume":"66","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026032712182334900_ref261","article-title":"Some improvements on locally repairable codes","volume":"abs\/1506.04822","author":"Zhang","year":"2015","journal-title":"CoRR"},{"key":"2026032712182334900_ref262","first-page":"334","article-title":"Two families of LRCs with availability based on iterative matrix","volume-title":"Proc. 13th International Symposium on Computational Intelligence and Design","author":"Zhang"},{"key":"2026032712182334900_ref263","article-title":"Explicit construction of minimum bandwidth rack-aware regenerating codes","volume":"abs\/2103.01533","author":"Zhou","year":"2021","journal-title":"CoRR"},{"issue":"4","key":"2026032712182334900_ref264","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/LCOMM.2014.030114.132694","article-title":"General fractional repetition codes for distributed storage systems","volume":"18","author":"Zhu","year":"2014","journal-title":"IEEE Commun. Lett."},{"issue":"7","key":"2026032712182334900_ref265","doi-asserted-by":"crossref","first-page":"4180","DOI":"10.1109\/TIT.2019.2898660","article-title":"Centralized multi-node repair regenerating codes","volume":"65","author":"Zorgui","year":"2019","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Foundations and Trends\u00ae in Communications and Information Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/19\/4\/547\/11097881\/0100000115en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/19\/4\/547\/11097881\/0100000115en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T14:10:44Z","timestamp":1777471844000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftcit\/article\/19\/4\/547\/1330348\/Codes-for-Distributed-Storage"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,30]]},"references-count":265,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,5,30]]}},"URL":"https:\/\/doi.org\/10.1561\/0100000115","relation":{},"ISSN":["1567-2190","1567-2328"],"issn-type":[{"value":"1567-2190","type":"print"},{"value":"1567-2328","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,30]]}}}