{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T21:05:05Z","timestamp":1758056705174,"version":"3.44.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T00:00:00Z","timestamp":1748995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s10623-025-01653-5","type":"journal-article","created":{"date-parts":[[2025,6,4]],"date-time":"2025-06-04T09:12:25Z","timestamp":1749028345000},"page":"3593-3618","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A class of locally recoverable codes over finite chain rings"],"prefix":"10.1007","volume":"93","author":[{"given":"Giulia","family":"Cavicchioni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eleonora","family":"Guerrini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessio","family":"Meneghetti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"issue":"1","key":"1653_CR1","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1109\/TIT.2004.839546","volume":"51","author":"MA Armand","year":"2005","unstructured":"Armand M.A.: List decoding of generalized Reed-Solomon codes over commutative rings. IEEE Trans. Inf. Theory 51(1), 411\u2013419 (2005).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR2","doi-asserted-by":"crossref","unstructured":"Barg A., Haymaker K., Howe E.W., Matthews G.L., V\u00e1rilly-Alvarado A.: Locally recoverable codes from algebraic curves and surfaces. In: Algebraic Geometry for Coding Theory and Cryptography: IPAM, February 2016, pp. 95\u2013127. Springer, Los Angeles (2017).","DOI":"10.1007\/978-3-319-63931-4_4"},{"issue":"11","key":"1653_CR3","doi-asserted-by":"publisher","first-page":"5787","DOI":"10.1109\/TIT.2015.2477406","volume":"61","author":"VR Cadambe","year":"2015","unstructured":"Cadambe V.R., Mazumdar A.: Bounds on the size of locally recoverable codes. IEEE Trans. Inf. Theory 61(11), 5787\u20135794 (2015).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR4","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.disc.2014.01.016","volume":"324","author":"M Forbes","year":"2014","unstructured":"Forbes M., Yekhanin S.: On the locality of codeword symbols in non-linear codes. Discret. Math. 324, 78\u201384 (2014).","journal-title":"Discret. Math."},{"issue":"11","key":"1653_CR5","doi-asserted-by":"publisher","first-page":"6925","DOI":"10.1109\/TIT.2012.2208937","volume":"58","author":"P Gopalan,","year":"2012","unstructured":"Gopalan, P., Huang, C., Simitci, H., Yekhanin, S.: On the locality of codeword symbols. IEEE Trans. Inf. Theory 58(11), 6925\u20136934 (2012).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR6","doi-asserted-by":"crossref","unstructured":"Goparaju S., Calderbank R.: Binary cyclic codes that are locally repairable. In: 2014 IEEE International Symposium on Information Theory, pp. 676\u2013680. IEEE (2014).","DOI":"10.1109\/ISIT.2014.6874918"},{"issue":"6","key":"1653_CR7","doi-asserted-by":"publisher","first-page":"3662","DOI":"10.1109\/TIT.2019.2891765","volume":"65","author":"V Guruswami,","year":"2019","unstructured":"Guruswami, V., Xing C., Yuan, C.: How long can optimal locally repairable codes be? IEEE Trans. Inf. Theory 65(6), 3662\u20133670 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"1653_CR8","doi-asserted-by":"publisher","first-page":"4658","DOI":"10.1109\/TIT.2019.2901492","volume":"65","author":"L Jin,","year":"2019","unstructured":"Jin, L.: Explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes. IEEE Trans. Inf. Theory 65(8), 4658\u20134663 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"1653_CR9","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1109\/TIT.2019.2946637","volume":"66","author":"L Jin,","year":"2019","unstructured":"Jin, L., Ma, L., Xing, C.: Construction of optimal locally repairable codes via automorphism groups of rational function fields. IEEE Trans. Inf. Theory 66(1), 210\u2013221 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"1653_CR10","doi-asserted-by":"publisher","first-page":"4637","DOI":"10.1109\/TIT.2014.2329872","volume":"60","author":"GM Kamath,","year":"2014","unstructured":"Kamath, G.M., Prakash, N., Lalitha, V., Kumar, P.V.: Codes with local regeneration and erasure correction. IEEE Trans. Inf. Theory 60(8), 4637\u20134660 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"1653_CR11","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1109\/TIT.2017.2713245","volume":"64","author":"J Liu,","year":"2017","unstructured":"Liu, J., Mesnager S., Chen, L.: New constructions of optimal locally recoverable codes via good polynomials. IEEE Trans. Inf. Theory 64(2), 889\u2013899 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR12","unstructured":"MacWilliams F.J., Sloane N.J.A.: The Theory of Error Correcting Codes, vol.\u00a016. Elsevier (1977)."},{"key":"1653_CR13","unstructured":"McDonald B.R.: Finite Rings with Identity, vol.\u00a028. Marcel Dekker Incorporated (1974)."},{"issue":"1","key":"1653_CR14","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1109\/TIT.2019.2939464","volume":"66","author":"G Micheli,","year":"2019","unstructured":"Micheli, G.: Constructions of locally recoverable codes which are optimal. IEEE Trans. Inf. Theory 66(1), 167\u2013175 (2019).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"3","key":"1653_CR15","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1109\/18.841186","volume":"46","author":"G Norton,","year":"2000","unstructured":"Norton, G., S\u0103l\u0103gean, A.: On the Hamming distance of linear codes over a finite chain ring. IEEE Trans. Inf. Theory 46(3), 1060\u20131067 (2000).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR16","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/PL00012382","volume":"10","author":"GH Norton,","year":"2000","unstructured":"Norton, G.H., S\u0103l\u0103gean A.: On the structure of linear and cyclic codes over a finite chain ring. Appl. Algebra Eng. Commun. Comput. 10, 489\u2013506 (2000).","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"2","key":"1653_CR17","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s10623-008-9220-8","volume":"50","author":"YH Park,","year":"2009","unstructured":"Park, Y.H.: Modular independence and generator matrices for codes over $${\\mathbb{Z} }_m$$. Des. Codes Cryptogr. 50(2), 147\u2013162 (2009).","journal-title":"Des. Codes Cryptogr."},{"key":"1653_CR18","doi-asserted-by":"crossref","unstructured":"Prakash N., Kamath G.M., Lalitha V., Kumar P.V.: Optimal linear codes with a local-error-correction property. In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 2776\u20132780. IEEE (2012).","DOI":"10.1109\/ISIT.2012.6284028"},{"issue":"9","key":"1653_CR19","doi-asserted-by":"publisher","first-page":"5882","DOI":"10.1109\/TIT.2013.2264797","volume":"59","author":"G Quintin,","year":"2013","unstructured":"Quintin, G., Barbier M., Chabot, C.: On generalized Reed\u2013Solomon codes over commutative and noncommutative rings. IEEE Trans. Inf. Theory 59(9), 5882\u20135897 (2013).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"1653_CR20","doi-asserted-by":"publisher","first-page":"4481","DOI":"10.1109\/TIT.2016.2524510","volume":"62","author":"AS Rawat,","year":"2016","unstructured":"Rawat, A.S., Papailiopoulos, D.S., Dimakis A.G., Vishwanath, S.: Locality and availability in distributed storage. IEEE Trans. Inf. Theory 62(8), 4481\u20134493 (2016).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1653_CR21","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1023\/A:1008767703006","volume":"12","author":"K Shiromoto,","year":"2000","unstructured":"Shiromoto, K.: Singleton bounds for codes over finite rings. J. Algebraic Combin. 12, 95\u201399 (2000).","journal-title":"J. Algebraic Combin."},{"issue":"8","key":"1653_CR22","doi-asserted-by":"publisher","first-page":"4661","DOI":"10.1109\/TIT.2014.2321280","volume":"60","author":"I Tamo,","year":"2014","unstructured":"Tamo, I., Barg, A.: A family of optimal locally recoverable codes. IEEE Trans. Inf. Theory 60(8), 4661\u20134676 (2014).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"1653_CR23","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s10623-022-01099-z","volume":"91","author":"P Tan,","year":"2023","unstructured":"Tan, P., Fan, C., Ding, C., Tang C., Zhou, Z.: The minimum locality of linear codes. Des. Codes Cryptogr. 91(1), 83\u2013114 (2023).","journal-title":"Des. Codes Cryptogr."},{"key":"1653_CR24","volume-title":"Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities","author":"JA Wood","year":"2009","unstructured":"Wood J.A.: Foundations of Linear Codes Defined over Finite Modules: The Extension Theorem and the MacWilliams Identities. World Scientific, Singapore (2009)."},{"key":"1653_CR25","unstructured":"Xing C., Yuan C.: Construction of optimal locally recoverable codes and connection with hypergraph. arXiv preprint (2018). arXiv:1811.09142."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01653-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01653-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01653-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T17:30:42Z","timestamp":1757957442000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01653-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,4]]},"references-count":25,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["1653"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01653-5","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2025,6,4]]},"assertion":[{"value":"14 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}