A generalization of the Tang-Ding binary cyclic codes

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-01-21 DOI:10.1016/j.disc.2024.114390

Ling Li , Minjia Shi , Sihui Tao , Zhonghua Sun , Shixin Zhu , Jon-Lark Kim , Patrick Solé

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引用次数: 0

Abstract

Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory and practice. Recently, Tang and Ding (2022) [34] proposed an infinite family of binary cyclic codes with good parameters. Shi et al. [arXiv:2309.12003v1, 2023] extended the binary Tang-Ding codes to the 4-ary case. Inspired by these two works, we study

2^{s}

-ary Tang-Ding codes, where

s \geq 2

. Good lower bounds on the minimum distance of the

2^{s}

-ary Tang-Ding codes are presented. As a by-product, an infinite family of

2^{s}

-ary duadic codes with a square-root like lower bound is presented.

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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.