{"title":"Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings","authors":"H. Dinh, Hualu Liu, R. Tansuchat, Thang M. Vo","doi":"10.1142/s1005386721000468","DOIUrl":null,"url":null,"abstract":"Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"154 4","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386721000468","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].
期刊介绍：
Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.
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