{"title":"Combinatorial Constructions of Optimal Quaternary Additive Codes","authors":"Chaofeng Guan;Jingjie Lv;Gaojun Luo;Zhi Ma","doi":"10.1109/TIT.2024.3467123","DOIUrl":null,"url":null,"abstract":"This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive \n<inline-formula> <tex-math>$[n,3.5,n-t]_{4}$ </tex-math></inline-formula>\n codes for all t with variable n, except for \n<inline-formula> <tex-math>$t=6,7,12$ </tex-math></inline-formula>\n.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7690-7700"},"PeriodicalIF":2.2000,"publicationDate":"2024-09-24","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/10693309/","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
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive
$[n,3.5,n-t]_{4}$
codes for all t with variable n, except for
$t=6,7,12$
.
本文旨在构建非整数维的最优四元加法码。首先，我们提出了四元加法恒重码的组合构造，以及加法广义反码构造。随后，我们提出了广义构造 X，它有助于从线性码构造非整数维最优加法码。然后，我们通过这两种方法构建了十类最优四元非整数维加法码。作为应用，我们还确定了除 $t=6,7,12$ 外，所有 t 的可变 n 的最优加法码 $[n,3.5,n-t]_{4}$ 。
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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