{"title":"On the square code of group codes","authors":"Alejandro Piñera Nicolás , Ignacio Fernández Rúa , Adriana Suárez Corona","doi":"10.1016/j.ffa.2024.102548","DOIUrl":null,"url":null,"abstract":"<div><div>Error correcting codes have recently gained more attention due to their applications in quantum resistant cryptography. Their suitability depends on their indistinguishability from random codes. In that sense, the study of the square code of a particular code provides a tool for distinguishing random codes from not random ones.</div><div>With this motivation, the square codes of some semisimple bilateral group codes, as abelian and dihedral ones, are studied in this paper. For this purpose, bilateral group codes are described as evaluation codes by means of the absolutely irreducible characters of the group. Finally, some results on self-duality and self-orthogonality are recovered under this alternative point of view.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"103 ","pages":"Article 102548"},"PeriodicalIF":1.2000,"publicationDate":"2024-12-10","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/S1071579724001874","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
Error correcting codes have recently gained more attention due to their applications in quantum resistant cryptography. Their suitability depends on their indistinguishability from random codes. In that sense, the study of the square code of a particular code provides a tool for distinguishing random codes from not random ones.
With this motivation, the square codes of some semisimple bilateral group codes, as abelian and dihedral ones, are studied in this paper. For this purpose, bilateral group codes are described as evaluation codes by means of the absolutely irreducible characters of the group. Finally, some results on self-duality and self-orthogonality are recovered under this alternative point of view.
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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