A Note on the Decomposition of Cyclic Codes into Cyclic Classes

The problem of finding the cycle representatives of a cyclic code is considered. In a recent paper, Tavares, Allard and Shiva, provided a solution to this problem for all cyclic codes having a parity check polynomial which satisfies either of the following conditions: (i) h ( x ) consists entirely of factors having exponent n , (ii) the exponents of the factors of h ( x ) are relatively prime to each other. For other cyclic codes, the solution remained incomplete. In this paper we provide a complete solution of the problem.