A generalization of the Tang-Ding binary cyclic codes

초록

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 2s-ary Tang-Ding codes, where s >= 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. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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