有限域上的自偶 2-quasi 负环码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-11-07 DOI:10.1016/j.ffa.2024.102541

Yun Fan, Yue Leng

{"title":"有限域上的自偶 2-quasi 负环码","authors":"Yun Fan, Yue Leng","doi":"10.1016/j.ffa.2024.102541","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the existence and asymptotic properties of self-dual 2-quasi negacyclic codes of length 2<em>n</em> over a finite field of cardinality <em>q</em>. When <em>n</em> is odd, we show that the <em>q</em>-ary self-dual 2-quasi negacyclic codes exist if and only if <span><math><mi>q</mi><mspace></mspace><mo>≢</mo><mo>−</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span>. When <em>n</em> is even, we prove that the <em>q</em>-ary self-dual 2-quasi negacyclic codes always exist. By using the technique introduced in this paper, we prove that <em>q</em>-ary self-dual 2-quasi negacyclic codes are asymptotically good.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"101 ","pages":"Article 102541"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Self-dual 2-quasi negacyclic codes over finite fields\",\"authors\":\"Yun Fan, Yue Leng\",\"doi\":\"10.1016/j.ffa.2024.102541\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we investigate the existence and asymptotic properties of self-dual 2-quasi negacyclic codes of length 2<em>n</em> over a finite field of cardinality <em>q</em>. When <em>n</em> is odd, we show that the <em>q</em>-ary self-dual 2-quasi negacyclic codes exist if and only if <span><math><mi>q</mi><mspace></mspace><mo>≢</mo><mo>−</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span>. When <em>n</em> is even, we prove that the <em>q</em>-ary self-dual 2-quasi negacyclic codes always exist. By using the technique introduced in this paper, we prove that <em>q</em>-ary self-dual 2-quasi negacyclic codes are asymptotically good.</div></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":\"101 \",\"pages\":\"Article 102541\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-07\",\"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/S1071579724001801\",\"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/S1071579724001801","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

当 n 为奇数时，我们证明了当且仅当 q≢-1(mod4)时 q-ary 自双 2-quasi 负环码存在。当 n 为偶数时，我们证明 q-ary 自双 2-quasi 负环码总是存在的。利用本文介绍的技术，我们证明了 qary 自双 2-quasi 负环码是渐近良好的。

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

Self-dual 2-quasi negacyclic codes over finite fields

In this paper, we investigate the existence and asymptotic properties of self-dual 2-quasi negacyclic codes of length 2n over a finite field of cardinality q. When n is odd, we show that the q-ary self-dual 2-quasi negacyclic codes exist if and only if

q ≢ - 1 (\mod 4)

. When n is even, we prove that the q-ary self-dual 2-quasi negacyclic codes always exist. By using the technique introduced in this paper, we prove that q-ary self-dual 2-quasi negacyclic codes are asymptotically good.

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.