Constacyclic Codes of Length 3ps Over Fpm + uFpm and Their Application in Various Distance Distributions

Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3p
^s
over the finite commutative chain ring Fp
^m
+ uFp
^m
(u
²
= 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 3p
^s
over Fp
^m
+ uFp
^m
(u
²
= 0) be an MDS constacyclic code with respect to Hamming distance is provided.