{"title":"A class of double-twisted generalized Reed-Solomon codes","authors":"Canze Zhu , Qunying Liao","doi":"10.1016/j.ffa.2024.102395","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, let <em>q</em> be a prime power, we focus on a class of double-twisted generalized Reed-Solomon code <span><math><mi>C</mi></math></span> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>. We give a sufficient and necessary condition for <span><math><mi>C</mi></math></span> to be MDS or AMDS, and prove that <span><math><mi>C</mi></math></span> is non-GRS by calculating the Schur square of its dual code. Furthermore, we present a sufficient and necessary condition for <span><math><mi>C</mi></math></span> to be self-dual, and then construct several classes of self-dual NMDS or non-GRS MDS codes.</p></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1071579724000340","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, let q be a prime power, we focus on a class of double-twisted generalized Reed-Solomon code over . We give a sufficient and necessary condition for to be MDS or AMDS, and prove that is non-GRS by calculating the Schur square of its dual code. Furthermore, we present a sufficient and necessary condition for to be self-dual, and then construct several classes of self-dual NMDS or non-GRS MDS codes.
期刊介绍：
Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering.
For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods.
The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
