Four classes of optimal p-ary cyclic codes
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 [pm-1,pm-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 pm+1/2 with parameters [pm-1,pm-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 [5m-1,5m-2m-2,4] are special cases of the codes constructed in this paper.
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