{"title":"On the minimum weights of quaternary Hermitian LCD codes","authors":"Makoto Araya, Masaaki Harada","doi":"10.1007/s12095-024-00733-y","DOIUrl":null,"url":null,"abstract":"<p>We study the largest minimum weights among quaternary Hermitian LCD codes. We determine the largest minimum weights among quaternary Hermitian LCD codes of length <i>n</i> and dimension <i>k</i> for <span>\\(k \\le n \\le 17\\)</span>. A quaternary Hermitian LCD [21, 5, 13] code and a quaternary Hermitian LCD [21, 9, 9] code are also constructed for the first time. An updated table of the largest minimum weights among quaternary Hermitian LCD [<i>n</i>, <i>k</i>] codes is also given for <span>\\(k \\le n \\le 30\\)</span>.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography and Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12095-024-00733-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the largest minimum weights among quaternary Hermitian LCD codes. We determine the largest minimum weights among quaternary Hermitian LCD codes of length n and dimension k for \(k \le n \le 17\). A quaternary Hermitian LCD [21, 5, 13] code and a quaternary Hermitian LCD [21, 9, 9] code are also constructed for the first time. An updated table of the largest minimum weights among quaternary Hermitian LCD [n, k] codes is also given for \(k \le n \le 30\).
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