满足Griesmer界或具有最优最小距离的二进制自正交码

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2025-02-28 DOI:10.1016/j.jcta.2025.106027

Minjia Shi , Shitao Li , Tor Helleseth , Jon-Lark Kim

{"title":"满足Griesmer界或具有最优最小距离的二进制自正交码","authors":"Minjia Shi , Shitao Li , Tor Helleseth , Jon-Lark Kim","doi":"10.1016/j.jcta.2025.106027","DOIUrl":null,"url":null,"abstract":"<div><div>The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing the Solomon-Stiffler codes. As a result, we reduce a problem with an infinite number of cases to a finite number of cases. Second, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code. Using such a characterization, we completely determine the exact value of <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>o</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mn>7</mn><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>o</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> denotes the largest minimum distance among all binary self-orthogonal <span><math><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>]</mo></math></span> codes.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"214 ","pages":"Article 106027"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances\",\"authors\":\"Minjia Shi , Shitao Li , Tor Helleseth , Jon-Lark Kim\",\"doi\":\"10.1016/j.jcta.2025.106027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing the Solomon-Stiffler codes. As a result, we reduce a problem with an infinite number of cases to a finite number of cases. Second, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code. Using such a characterization, we completely determine the exact value of <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>o</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mn>7</mn><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>o</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span> denotes the largest minimum distance among all binary self-orthogonal <span><math><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>]</mo></math></span> codes.</div></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":\"214 \",\"pages\":\"Article 106027\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316525000226\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316525000226","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文的目的是双重的。首先，我们利用solomon - stiff码刻画了满足Griesmer界的二进制自正交码的存在性。因此，我们将一个有无限种情况的问题简化为有限种情况。其次，通过考虑二进制自正交码的残差码，给出了证明某些二进制自正交码不存在的一般方法。利用这样的表征，我们完全确定了dso（n,7）的精确值，其中dso（n,k）表示所有二进制自正交[n，k]码之间的最大最小距离。

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

Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing the Solomon-Stiffler codes. As a result, we reduce a problem with an infinite number of cases to a finite number of cases. Second, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code. Using such a characterization, we completely determine the exact value of

d_{s o} (n, 7)

, where

d_{s o} (n, k)

denotes the largest minimum distance among all binary self-orthogonal

[n, k]

codes.

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

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.