{"title":"Four families of q-ary self-orthogonal codes via the defining-set construction","authors":"Jiayuan Zhang, Xiaoshan Kai, Ping Li, Shixin Zhu","doi":"10.1016/j.ffa.2025.102586","DOIUrl":null,"url":null,"abstract":"<div><div>Self-orthogonal codes have a wide range of applications in various fields, especially communication and cryptography. In this paper, we construct four families of linear codes over finite fields via a defining-set construction. The weight distributions of these codes are determined. We show that most of these codes are self-orthogonal and reach the Grismer bound.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"104 ","pages":"Article 102586"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-13","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/S1071579725000164","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
Self-orthogonal codes have a wide range of applications in various fields, especially communication and cryptography. In this paper, we construct four families of linear codes over finite fields via a defining-set construction. The weight distributions of these codes are determined. We show that most of these codes are self-orthogonal and reach the Grismer bound.
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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