{"title":"Some q-ary constacyclic BCH codes with length qm+12","authors":"Jin Li , Huilian Zhu , Shixin Zhu","doi":"10.1016/j.ffa.2024.102545","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study some <em>q</em>-ary <em>λ</em>-constacyclic BCH codes of length <span><math><mfrac><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> with some large designed distances for <span><math><mrow><mi>ord</mi></mrow><mo>(</mo><mi>λ</mi><mo>)</mo><mo>=</mo><mn>2</mn></math></span> and <span><math><mn>2</mn><mo>+</mo><mo>⌈</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>q</mi><mo>−</mo><mn>3</mn></mrow></mfrac><mo>⌉</mo><mo>≤</mo><mrow><mi>ord</mi></mrow><mo>(</mo><mi>λ</mi><mo>)</mo><mo>≤</mo><mi>q</mi><mo>−</mo><mn>1</mn></math></span> respectively, where <em>q</em> is an odd prime power and <span><math><mrow><mi>ord</mi></mrow><mo>(</mo><mi>λ</mi><mo>)</mo><mo>|</mo><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. The dimensions and the lower bounds on the minimum distances of these codes are given by using recurrence relations and the introduced definitions of sequences. The code examples presented in this paper indicate that these codes have good parameters in general.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"102 ","pages":"Article 102545"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-21","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/S1071579724001849","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we study some q-ary λ-constacyclic BCH codes of length with some large designed distances for and respectively, where q is an odd prime power and . The dimensions and the lower bounds on the minimum distances of these codes are given by using recurrence relations and the introduced definitions of sequences. The code examples presented in this paper indicate that these codes have good parameters in general.
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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