Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fan, Jinmei, Feng, Jingyao, Men, Yuhan, Zhang, Yanhai
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7108226749
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