Constacyclic codes of length 3P^s over F<inf>P</inf>^M + UF<inf>P</inf>^M and their application in various distance distributions

Abstract

Let p 6= 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm(u2 = 0) are established in the term of their generator polynomials. As an application, Hamming and homogeneous distance of a class of such codes and RT distances of all are given. Among such λ-constacyclic codes, the unique maximum-distance-separable (briefly, MDS) code with respect to the RT distance is obtained. Moreover, when λ is not a cube in Fpm, the necessary and sufficient condition for the λ-constacyclic code of length 3ps over Fpm + uFpm(u2 = 0) be an MDS constacyclic code with respect to Hamming distance is provided.