Quasi-cyclic codes of index 2

IF 1.1 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2026-06-01 Epub Date: 2026-01-19 DOI:10.1016/j.disc.2026.115004

Kanat Abdukhalikov , Askar S. Dzhumadil'daev , San Ling

引用次数: 0

Abstract

We study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner products are investigated. We describe self-orthogonal and dual-containing codes. Lower bounds for minimum distances of quasi-cyclic codes are given. A quasi-cyclic code of index 2 is generated by at most two elements. We describe conditions when such a code (or its dual) is generated by one element.

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索引2的拟循环码

研究有限域上指标2的拟循环码。我们对这类代码进行了分类。研究了它们对欧几里得内积、辛内积和厄米内积的对偶。我们描述了自正交和双包含码。给出了拟循环码最小距离的下界。索引为2的拟循环码由最多两个元素生成。我们将描述由一个元素生成这种代码（或其对偶）的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.