有限域上循环码线性交集对的特征和构造

Somphong Jitman
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摘要

线性编码的线性交集对因其良好的代数特性和广泛的应用而备受关注。本文重点讨论有限域上循环码的线性交集对。本文提出了循环群中循环余集的一些性质,作为研究这类线性交集对的关键工具。根据两个循环码的生成多项式和循环余集,给出了固定相交维数的两个循环码的特征和构造。在理论表征的基础上,举例说明了一些具有良好参数的循环码线性交集对。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Characterizations and Constructions of Linear Intersection Pairs of Cyclic Codes over Finite Fields
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of cyclotomic cosets in cyclic groups are presented as key tools in the study of such linear intersection pairs. Characterization and constructions of two cyclic codes of a fixed intersecting dimension are given in terms of their generator polynomials and cyclotomic cosets. In some cases, constructions of two cyclic codes of a fixed intersecting subcode are presented as well. Based on the theoretical characterization, some numerical examples of linear intersection pairs of cyclic codes with good parameters are illustrated.
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