Four classes of optimal p-ary cyclic codes
Information Theory
2025-12-01 v1 math.IT
Abstract
Let p>3 be an odd prime and m be a positive integer. Little progress on the study of optimal p-ary cyclic codes with parameters [p^m-1,p^m-2m-2,4] has been made.In this paper, by weakening the necessary and sufficient conditions on cyclic codes to have codewords of Hamming weight 3 and analyzing the solutions of certain equations over finite fields, four classes of optimal p-ary cyclic codes deduced by p^m+1/2 with parameters [p^m-1,p^m-2m-2,4] are presented.Wherein three classes of optimal p-ary cyclic codes are infinite.Many classes of known optimal quinary cyclic codes with parameters [5^m-1,5^m-2m-2,4] are special cases of the codes constructed in this paper.
Keywords
Cite
@article{arxiv.2511.22086,
title = {Four classes of optimal p-ary cyclic codes},
author = {Jinmei Fan and Jingyao Feng and Yuhan Men and Yanhai Zhang},
journal= {arXiv preprint arXiv:2511.22086},
year = {2025}
}