Constacyclic codes of length ps over Fpm+uFpm

Abstract

For any prime p, all constacyclic codes of length ps over the ring R=Fpm+uFpm are considered. The units of the ring R are of the forms γ and α+uβ, where α,β, and γ are nonzero elements of Fpm, which provides pm(pm−1) such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length ps over the finite field Fpm are obtained; they are used as a tool to establish the structure and Hamming distances of all (α+uβ)-constacyclic codes of length ps over R. We then classify all cyclic codes of length ps over R and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and γ-constacyclic codes of length ps over R is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to γ-constacyclic codes of length ps over R.