{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T02:42:13Z","timestamp":1778553733181,"version":"3.51.4"},"reference-count":64,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"7","license":[{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["PHY-1415600"],"award-info":[{"award-number":["PHY-1415600"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"U.S. Army Research Office","doi-asserted-by":"publisher","award":["W911NF-14-1-0272"],"award-info":[{"award-number":["W911NF-14-1-0272"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["PHY-1416578"],"award-info":[{"award-number":["PHY-1416578"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1109\/tit.2017.2690381","type":"journal-article","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T19:00:14Z","timestamp":1490986814000},"page":"4675-4686","source":"Crossref","is-referenced-by-count":12,"title":["Distance Verification for Classical and Quantum LDPC Codes"],"prefix":"10.1109","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0884-9389","authenticated-orcid":false,"given":"Ilya","family":"Dumer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexey A.","family":"Kovalev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonid P.","family":"Pryadko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.838088"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.2585"},{"key":"ref33","author":"mackay","year":"2003","journal-title":"Information Theory Inference and Learning Algorithms"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1962.1057683"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/18.681315"},{"key":"ref30","first-page":"475","article-title":"Approximate algorithms for computing the minimum distance of low-density parity-check codes","author":"hu","year":"2004","journal-title":"Proc IEEE Int Symp Inf Theory"},{"key":"ref37","first-page":"3","article-title":"Complexity of decoding for linear codes","volume":"19","author":"evseev","year":"1983","journal-title":"Problemy Peredachi Informacii"},{"key":"ref36","first-page":"649","article-title":"Complexity issues in coding theory","author":"barg","year":"1998","journal-title":"Handbook of Coding Theory"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2167593"},{"key":"ref34","first-page":"987","article-title":"On the iterative decoding of sparse quantum codes","volume":"8","author":"poulin","year":"2008","journal-title":"Quant Inf Comput"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0019850"},{"key":"ref62","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/978-3-642-10366-7_6","article-title":"Security bounds for the design of codebased cryptosystems","volume":"5912","author":"finiasz","year":"2009","journal-title":"Journal of Cryptology (Lecture Notes in Computer Science)"},{"key":"ref61","first-page":"50","article-title":"On minimum distance decoding of linear codes","author":"dumer","year":"1991","journal-title":"Proc 5th Sov -Swedish Int Workshop Inf Theory"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22792-9_42"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/18.992777"},{"key":"ref64","first-page":"520","article-title":"Decoding random binary linear codes in 2n\/20: How 1 + 1 = 0 improves information set decoding","volume":"7237","author":"becker","year":"2012","journal-title":"Adv Cryptology"},{"key":"ref27","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/4347.001.0001","author":"gallager","year":"1963","journal-title":"Low Density Parity Check Codes"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2008.4595332"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.55.900"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.52.R2493"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.012311"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1063\/1.4891487"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1145\/2591796.2591870"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/18.641542"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035377.ch12"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536421"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2002.806118"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/18.57202"},{"key":"ref51","author":"erdos","year":"1974","journal-title":"Probabilistic Methods in Combinatorics"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2162642"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2009.5205662"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.820012"},{"key":"ref56","first-page":"50","article-title":"Weight distributions: How deviant can you be?","author":"di","year":"2001","journal-title":"Proc Int Symp Inf Theory (ISIT)"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/18.910575"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.928274"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.824918"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/18.910577"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.050503"},{"key":"ref11","author":"postol","year":"2001","journal-title":"A Proposed Quantum Low Density Parity Check Code"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2006.261958"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2004.834737"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.020304"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.050502"},{"key":"ref15","first-page":"799","article-title":"Quantum LDPC codes with positive rate and minimum distance proportional to n $^{1\/2}$","author":"tillich","year":"2009","journal-title":"Proc IEEE Int Symp Inf Theory (ISIT)"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01877-0_21"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2013.2261116"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/ISIT.2012.6284206"},{"key":"ref19","article-title":"New constructions of CSS codes obtained by moving to higher alphabets","author":"andriyanova","year":"0"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-4916(02)00018-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.3824"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.180501"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1499754"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1063\/1.2731356"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.012305"},{"key":"ref49","first-page":"103","article-title":"Decoding complexity bound for linear block codes","volume":"25","author":"kruk","year":"1989","journal-title":"Problemy Peredachi Informatsii"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.190504"},{"key":"ref46","article-title":"A public-key cryptosystem based on algebraic coding theory","author":"mceliece","year":"0"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1962.1057777"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/18.21270"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/3-540-45961-8_25","article-title":"An observation on the security of McEliece’s public-key cryptosystem","volume":"330","author":"lee","year":"1988","journal-title":"Journal of Cryptology (Lecture Notes in Computer Science)"},{"key":"ref42","first-page":"24","article-title":"Two decoding algorithms for linear codes","volume":"25","author":"dumer","year":"1989","journal-title":"Problemy Peredachi Informacii"},{"key":"ref41","first-page":"157","article-title":"On syndrome decoding of linear codes","volume":"2","author":"dumer","year":"1986","journal-title":"Proc 4th All-Union Symp Redundancy Inf Syst"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.1098"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/18.904512"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/ieeexplore.ieee.org\/ielaam\/18\/7948883\/7891006-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/18\/7948883\/07891006.pdf?arnumber=7891006","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T18:52:46Z","timestamp":1649443966000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7891006\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7]]},"references-count":64,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.1109\/tit.2017.2690381","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7]]}}}