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.

翻译：设p>3为奇素数，m为正整数。关于参数为[p^m-1,p^m-2m-2,4]的最优p元循环码的研究进展甚微。本文通过弱化循环码具有汉明重量为3的码字的充要条件，并分析有限域上特定方程的解，提出了由p^m+1/2导出的四类参数为[p^m-1,p^m-2m-2,4]的最优p元循环码。其中三类最优p元循环码是无限的。许多已知的参数为[5^m-1,5^m-2m-2,4]的最优五元循环码是本文所构造码的特例。