{"title":"Characterizations of the Minimum Weights of LCD Codes of Large Dimensions","authors":"Makoto Araya;Masaaki Harada;Keita Ishizuka;Yuto Tanaka","doi":"10.1109/TIT.2024.3483218","DOIUrl":null,"url":null,"abstract":"We give new characterizations of the largest minimum weights among LCD codes of large dimensions. Using the characterizations, we completely determine the largest minimum weights among binary LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-6$ </tex-math></inline-formula>\n, ternary LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-5$ </tex-math></inline-formula>\n and quaternary Hermitian LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-4$ </tex-math></inline-formula>\n for arbitrary n. We also determine the largest minimum weights among binary LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-7$ </tex-math></inline-formula>\n, ternary LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-6$ </tex-math></inline-formula>\n and quaternary Hermitian LCD codes of length n and dimension \n<inline-formula> <tex-math>$n-5$ </tex-math></inline-formula>\n with only some exceptions n.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8758-8769"},"PeriodicalIF":2.2000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10721596/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
We give new characterizations of the largest minimum weights among LCD codes of large dimensions. Using the characterizations, we completely determine the largest minimum weights among binary LCD codes of length n and dimension
$n-6$
, ternary LCD codes of length n and dimension
$n-5$
and quaternary Hermitian LCD codes of length n and dimension
$n-4$
for arbitrary n. We also determine the largest minimum weights among binary LCD codes of length n and dimension
$n-7$
, ternary LCD codes of length n and dimension
$n-6$
and quaternary Hermitian LCD codes of length n and dimension
$n-5$
with only some exceptions n.
期刊介绍：
The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.
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