准循环码的新距离界限

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-08-14 DOI:10.1007/s10623-024-01464-0

Ferruh Özbudak, Buket Özkaya

{"title":"准循环码的新距离界限","authors":"Ferruh Özbudak, Buket Özkaya","doi":"10.1007/s10623-024-01464-0","DOIUrl":null,"url":null,"abstract":"<p>We consider the minimum weight of codewords in a quasi-cyclic code and characterize the estimate in its most general setup using their concatenated structure. The new bound we derive generalizes the Jensen and Güneri–Özbudak bounds and it holds for the more general class of multilevel concatenated codes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"18 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New distance bounds for quasi-cyclic codes\",\"authors\":\"Ferruh Özbudak, Buket Özkaya\",\"doi\":\"10.1007/s10623-024-01464-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider the minimum weight of codewords in a quasi-cyclic code and characterize the estimate in its most general setup using their concatenated structure. The new bound we derive generalizes the Jensen and Güneri–Özbudak bounds and it holds for the more general class of multilevel concatenated codes.</p>\",\"PeriodicalId\":11130,\"journal\":{\"name\":\"Designs, Codes and Cryptography\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Designs, Codes and Cryptography\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10623-024-01464-0\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-024-01464-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了准循环码中码字的最小权重，并利用它们的串联结构描述了最一般情况下的估计值。我们推导出的新界限概括了詹森界限和居内利-厄兹布达克界限，它适用于更一般的多级连接码。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

New distance bounds for quasi-cyclic codes

We consider the minimum weight of codewords in a quasi-cyclic code and characterize the estimate in its most general setup using their concatenated structure. The new bound we derive generalizes the Jensen and Güneri–Özbudak bounds and it holds for the more general class of multilevel concatenated 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

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.