{"title":"Double circulant codes from cubic cyclotomy","authors":"Minjia Shi , Xinpeng Bian , Patrick Solé","doi":"10.1016/j.ffa.2025.102593","DOIUrl":null,"url":null,"abstract":"<div><div>We introduce a parametrized family of binary double circulant codes, based on cubic cyclotomy. We determine the parameters for which the codes are self-dual and those for which they are LCD (Linear Complementary Dual). As a bonus, they turn out to be formally self-dual in the latter case. The main theoretical tools are the properties of cyclotomic numbers. Examples in modest length show quasi-optimal formally self-dual codes.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"104 ","pages":"Article 102593"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-24","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/S1071579725000231","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
Abstract
We introduce a parametrized family of binary double circulant codes, based on cubic cyclotomy. We determine the parameters for which the codes are self-dual and those for which they are LCD (Linear Complementary Dual). As a bonus, they turn out to be formally self-dual in the latter case. The main theoretical tools are the properties of cyclotomic numbers. Examples in modest length show quasi-optimal formally self-dual codes.
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.
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