{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:18:42Z","timestamp":1787239122874,"version":"3.56.0"},"reference-count":30,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["22K03410"],"award-info":[{"award-number":["22K03410"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006134","name":"Foundation for Promotion of Material Science and Technology of Japan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006134","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Croatian Science Foundation","doi-asserted-by":"publisher","award":["HRZZ-IP-2022-10-4571"],"award-info":[{"award-number":["HRZZ-IP-2022-10-4571"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Croatian Science Foundation","doi-asserted-by":"publisher","award":["HRZZ-UIP-2020-02-5713"],"award-info":[{"award-number":["HRZZ-UIP-2020-02-5713"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["25K17290"],"award-info":[{"award-number":["25K17290"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.disc.2026.115066","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T10:55:23Z","timestamp":1771930523000},"page":"115066","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"title":["Constructions of self-orthogonal and LCD subspace codes"],"prefix":"10.1016","volume":"349","author":[{"given":"Dean","family":"Crnkovi\u0107","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keita","family":"Ishizuka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hadi","family":"Kharaghani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sho","family":"Suda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6558-5167","authenticated-orcid":false,"given":"Andrea","family":"\u0160vob","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.disc.2026.115066_br0010","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"},{"key":"10.1016\/j.disc.2026.115066_br0020","first-page":"951","article-title":"Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach","volume":"304","author":"Araya","year":"2017","journal-title":"Math. Comput."},{"key":"10.1016\/j.disc.2026.115066_br0030","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1080\/03081087.2019.1572708","article-title":"On equitable partition of matrices and its applications","volume":"68","author":"Atik","year":"2020","journal-title":"Linear Multilinear Algebra"},{"key":"10.1016\/j.disc.2026.115066_br0040","series-title":"Algebraic Combinatorics I: Association Schemes","author":"Bannai","year":"1984"},{"issue":"1","key":"10.1016\/j.disc.2026.115066_br0050","doi-asserted-by":"crossref","DOI":"10.1007\/s00022-021-00572-9","article-title":"Improvement to the sunflower bound for a class of equidistant constant dimension subspace codes","volume":"112","author":"Bartoli","year":"2021","journal-title":"J. Geom."},{"key":"10.1016\/j.disc.2026.115066_br0060","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0378-3758(77)90008-8","article-title":"Symmetric group divisible designs with the dual property","volume":"1","author":"Bose","year":"1977","journal-title":"J. Stat. Plan. Inference"},{"key":"10.1016\/j.disc.2026.115066_br0070","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1016\/j.disc.2018.01.018","article-title":"Orbit matrices of Hadamard matrices and related codes","volume":"341","author":"Crnkovi\u0107","year":"2018","journal-title":"Discrete Math."},{"issue":"3","key":"10.1016\/j.disc.2026.115066_br0080","first-page":"225","article-title":"New constructions of Deza digraphs","volume":"13","author":"Crnkovi\u0107","year":"2024","journal-title":"Int. J. Group Theory"},{"key":"10.1016\/j.disc.2026.115066_br0090","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s10801-021-01104-z","article-title":"Self-orthogonal codes from equitable partitions of association schemes","volume":"55","author":"Crnkovi\u0107","year":"2022","journal-title":"J. Algebr. Comb."},{"key":"10.1016\/j.disc.2026.115066_br0100","doi-asserted-by":"crossref","first-page":"3215","DOI":"10.1007\/s10623-023-01251-3","article-title":"LCD subspace codes","volume":"91","author":"Crnkovi\u0107","year":"2023","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/j.disc.2026.115066_br0110","doi-asserted-by":"crossref","DOI":"10.1007\/s00373-024-02763-y","article-title":"Self-orthogonal codes from Deza graphs, normally regular digraphs and Deza digraphs","volume":"40","author":"Crnkovi\u0107","year":"2024","journal-title":"Graphs Comb."},{"key":"10.1016\/j.disc.2026.115066_br0120","series-title":"Network Coding and Subspace Designs, Signals and Communication Technology","year":"2018"},{"key":"10.1016\/j.disc.2026.115066_br0130","doi-asserted-by":"crossref","first-page":"978","DOI":"10.1016\/j.jcta.2010.10.003","article-title":"Divisible design graphs","volume":"118","author":"Haemers","year":"2011","journal-title":"J. Comb. Theory, Ser. A"},{"key":"10.1016\/j.disc.2026.115066_br0140","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0012-365X(02)00553-8","article-title":"Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms","volume":"264","author":"Harada","year":"2003","journal-title":"Discrete Math."},{"key":"10.1016\/j.disc.2026.115066_br0150","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10623-018-0544-8","article-title":"Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6","volume":"87","author":"Heinlein","year":"2019","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/j.disc.2026.115066_br0160","doi-asserted-by":"crossref","first-page":"4413","DOI":"10.1109\/TIT.2006.881746","article-title":"A random linear network coding approach to multicast","volume":"52","author":"Ho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/j.disc.2026.115066_br0170","series-title":"Combinatorics and Graphs","first-page":"243","article-title":"On the real unbiased Hadamard matrices","volume":"vol. 531","author":"Holzmann","year":"2010"},{"key":"10.1016\/j.disc.2026.115066_br0180","series-title":"Fundamentals of Error-Correcting Codes","author":"Huffman","year":"2003"},{"key":"10.1016\/j.disc.2026.115066_br0190","series-title":"Combinatorics '90","first-page":"275","article-title":"Coset enumeration in groups and constructions of symmetric designs","volume":"vol. 52","author":"Janko","year":"1992"},{"issue":"3","key":"10.1016\/j.disc.2026.115066_br0200","article-title":"Mutually unbiased Bush-type Hadamard matrices and association schemes","volume":"22","author":"Kharaghani","year":"2015","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.disc.2026.115066_br0210","series-title":"Mathematics Across Contemporary Sciences","first-page":"137","article-title":"Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes","volume":"vol. 190","author":"Kharaghani","year":"2017"},{"key":"10.1016\/j.disc.2026.115066_br0220","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10801-017-0777-z","article-title":"Linked systems of symmetric group divisible designs","volume":"47","author":"Kharaghani","year":"2017","journal-title":"J. Algebr. Comb."},{"key":"10.1016\/j.disc.2026.115066_br0230","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s10623-017-0414-9","article-title":"Unbiased orthogonal designs","volume":"86","author":"Kharaghani","year":"2018","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/j.disc.2026.115066_br0240","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1007\/s10623-019-00622-z","article-title":"Linked system of symmetric group divisible designs of type II","volume":"87","author":"Kharaghani","year":"2019","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/j.disc.2026.115066_br0250","doi-asserted-by":"crossref","first-page":"3579","DOI":"10.1109\/TIT.2008.926449","article-title":"Coding for errors and erasures in random network coding","volume":"54","author":"K\u00f6tter","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/j.disc.2026.115066_br0260","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.laa.2021.03.019","article-title":"A stability result and a spectrum result on constant dimension codes","volume":"621","author":"Lucas","year":"2021","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.disc.2026.115066_br0270","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0012-365X(92)90563-U","article-title":"Linear codes with complementary duals","volume":"106\/107","author":"Massey","year":"1992","journal-title":"Discrete Math."},{"key":"10.1016\/j.disc.2026.115066_br0280","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10801-015-0581-6","article-title":"Weighing matrices and spherical codes","volume":"42","author":"Nozaki","year":"2015","journal-title":"J. Algebr. Comb."},{"key":"10.1016\/j.disc.2026.115066_br0290","doi-asserted-by":"crossref","first-page":"3951","DOI":"10.1109\/TIT.2008.928291","article-title":"A rank-metric approach to error control in random network coding","volume":"54","author":"Silva","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"10.1016\/j.disc.2026.115066_br0300","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s12095-020-00463-x","article-title":"Further constructions of cyclic subspace codes","volume":"13","author":"Zhang","year":"2021","journal-title":"Cryptogr. Commun."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X26000907?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X26000907?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:03:33Z","timestamp":1777442613000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X26000907"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":30,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0012365X26000907"],"URL":"https:\/\/doi.org\/10.1016\/j.disc.2026.115066","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Constructions of self-orthogonal and LCD subspace codes","name":"articletitle","label":"Article Title"},{"value":"Discrete Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.disc.2026.115066","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115066"}}