Constructing self-dual cyclic codes over Z_9 of length 3n

摘要

In this paper, we study cyclic codes over Z_9 of length 3n, where n is a positive integer satisfying gcd(3, n) = 1. First, a canonical form decomposition of any cyclic code over Z_9 of length 3n are given and a unique set of generators for each subcode is presented. Hence the structure of any cyclic code over Z_9 of length 3n is determined. From this decomposition, formulas for the number of all codes and the number of codewords in each code are given. Then dual codes and self-duality of these codes are investigated. As an application, all 10061824 distinct cyclic codes over Z_9 of length 24 and all 544 self-dual codes among them are listed explicitly. Moreover, 280 new and good self-dual cyclic codes over Z_9 with basic parameters (24, 324, 3) are obtained.