Quasi-polycyclic and skew quasi-polycyclic codes over Fq

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-10-31 DOI:10.1016/j.ffa.2024.102536

Tushar Bag, Daniel Panario

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.

查看原文本刊更多论文

Fq 上的准多环码和偏斜准多环码

在这项研究中，我们的重点是研究域上的单生成器右准多环（QPC）码。我们详细描述了如何从 QPC 码中构造出具有可观最小距离的线性码。我们分析了各种内积下的对偶 QPC 码，并用它们来构造量子纠错码。此外，我们的研究还包括一个专门章节，深入探讨偏斜准多环（SQPC）码领域，研究它们的特性以及生成器在其构造中的作用。本节将我们的研究扩展到 SQPC 码这一引人入胜的领域，深入探讨 QPC 码的非交换版本、它们的特性和生成器结构。我们的研究涉及 QPC 码、斜多环码和 SQPC 码的结构特性，揭示了它们在增强编码理论领域的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

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.