两类双扭转广义Reed-Solomon码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-02-18 DOI:10.1016/j.ffa.2025.102595

Shudi Yang , Jinlong Wang , Yansheng Wu

{"title":"两类双扭转广义Reed-Solomon码","authors":"Shudi Yang , Jinlong Wang , Yansheng Wu","doi":"10.1016/j.ffa.2025.102595","DOIUrl":null,"url":null,"abstract":"<div><div>MDS codes, abbreviated from maximum distance separable codes, hold significant importance in coding theory owing to their good algebraic structures, alongside intriguing practical applications. In this paper, we mainly study two classes of twisted generalized Reed-Solomon codes with two twists. Specifically, some sufficient and necessary conditions for these codes to be MDS or self-orthogonal are obtained; two explicit constructions of MDS self-orthogonal codes are presented; and finally, several classes of linear complementary dual codes via twisted generalized Reed-Solomon codes are also provided.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"104 ","pages":"Article 102595"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two classes of twisted generalized Reed-Solomon codes with two twists\",\"authors\":\"Shudi Yang , Jinlong Wang , Yansheng Wu\",\"doi\":\"10.1016/j.ffa.2025.102595\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>MDS codes, abbreviated from maximum distance separable codes, hold significant importance in coding theory owing to their good algebraic structures, alongside intriguing practical applications. In this paper, we mainly study two classes of twisted generalized Reed-Solomon codes with two twists. Specifically, some sufficient and necessary conditions for these codes to be MDS or self-orthogonal are obtained; two explicit constructions of MDS self-orthogonal codes are presented; and finally, several classes of linear complementary dual codes via twisted generalized Reed-Solomon codes are also provided.</div></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":\"104 \",\"pages\":\"Article 102595\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-02-18\",\"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/S1071579725000255\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1071579725000255","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

摘要

MDS码是最大距离可分离码的缩写，由于其良好的代数结构和有趣的实际应用，在编码理论中具有重要意义。本文主要研究了两类具有两个扭转的广义Reed-Solomon码。具体地说，得到了这些码是MDS或自正交的一些充要条件；给出了MDS自正交码的两种显式结构；最后，通过扭曲广义Reed-Solomon码，给出了若干类线性互补对偶码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Two classes of twisted generalized Reed-Solomon codes with two twists

MDS codes, abbreviated from maximum distance separable codes, hold significant importance in coding theory owing to their good algebraic structures, alongside intriguing practical applications. In this paper, we mainly study two classes of twisted generalized Reed-Solomon codes with two twists. Specifically, some sufficient and necessary conditions for these codes to be MDS or self-orthogonal are obtained; two explicit constructions of MDS self-orthogonal codes are presented; and finally, several classes of linear complementary dual codes via twisted generalized Reed-Solomon codes are also provided.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

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.