通过穿刺和缩短最优循环码获得最优线性码的新类别

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-06 DOI:10.1007/s00200-024-00653-7

Félix Hernández, Gerardo Vega

{"title":"通过穿刺和缩短最优循环码获得最优线性码的新类别","authors":"Félix Hernández, Gerardo Vega","doi":"10.1007/s00200-024-00653-7","DOIUrl":null,"url":null,"abstract":"<p>In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes\",\"authors\":\"Félix Hernández, Gerardo Vega\",\"doi\":\"10.1007/s00200-024-00653-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures.</p>\",\"PeriodicalId\":50742,\"journal\":{\"name\":\"Applicable Algebra in Engineering Communication and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Algebra in Engineering Communication and Computing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s00200-024-00653-7\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Algebra in Engineering Communication and Computing","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00200-024-00653-7","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们在两类已知的最优循环码上使用了穿刺和缩短技术，从而得到了三类新的最优线性码，它们都达到了格里斯梅尔约束。这些码的权重分布已经确定。我们还对它们的对偶码进行了研究，结果表明这些对偶码要么是最优码，要么几乎是最优码，符合球形堆积约束。此外，这些对偶码还包含几乎最大距离可分离码的类别，并证明它们适用于错误检测。此外，所获得的一些最优线性编码适用于构建具有良好访问结构的秘密共享方案。

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

Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes

In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures.

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.