On the Hamming distances of repeated-root constacyclic codes of length [formula omitted

Abstract

Let p be an odd prime, s, m be positive integers, γ,λ be nonzero elements of the finite field Fpm such that γps=λ. In this paper, we show that, for any positive integer η, the Hamming distances of all repeated-root λ-constacyclic codes of length ηps can be determined by those of certain simple-root γ-constacyclic codes of length η. Using this result, Hamming distances of all constacyclic codes of length 4ps are obtained. As an application, we identify all MDS λ-constacyclic codes of length 4ps.