On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m

Abstract

Let p = 5 be any odd prime. Using the algebraic structures of all cyclic codes of length 5p s over the finite commutative chain ring R = F p m + uF p m , in this paper, the exact values of Hamming distances of all cyclic codes of length 5p s over R are established. As an application, we identify all maximal distance separable cyclic codes of length 5p s . INDEX TERMS Constacyclic codes, cyclic codes, dual codes, chain rings, Hamming distance, Singleton bound, MDS codes.