{"title":"Quasi-polycyclic and skew quasi-polycyclic codes over Fq","authors":"Tushar Bag, Daniel Panario","doi":"10.1016/j.ffa.2024.102536","DOIUrl":null,"url":null,"abstract":"<div><div>In this research, our focus is on investigating 1-generator right quasi-polycyclic (QPC) codes over fields. We provide a detailed description of how linear codes with substantial minimum distances can be constructed from QPC codes. We analyze dual QPC codes under various inner products and use them to construct quantum error-correcting codes. Furthermore, our research includes a dedicated section that delves into the area of skew quasi-polycyclic (SQPC) codes, investigating their properties and the role of generators in their construction. This section expands our study to encompass the intriguing area of SQPC codes, offering insights into the non-commutative version of QPC codes, their characteristics and generator structures. Our work deals with the structural properties of QPC, skew polycyclic and SQPC codes, shedding light on their potential for enhancing the field of coding theory.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-10-31","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/S1071579724001758","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
In this research, our focus is on investigating 1-generator right quasi-polycyclic (QPC) codes over fields. We provide a detailed description of how linear codes with substantial minimum distances can be constructed from QPC codes. We analyze dual QPC codes under various inner products and use them to construct quantum error-correcting codes. Furthermore, our research includes a dedicated section that delves into the area of skew quasi-polycyclic (SQPC) codes, investigating their properties and the role of generators in their construction. This section expands our study to encompass the intriguing area of SQPC codes, offering insights into the non-commutative version of QPC codes, their characteristics and generator structures. Our work deals with the structural properties of QPC, skew polycyclic and SQPC codes, shedding light on their potential for enhancing the field of coding theory.
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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