Repeated-root constacyclic codes of prime power length over Fpm[u]〈ua〉 and their duals

The units of the chain ring Ra=Fpm[u]〈ua〉=Fpm+uFpm+⋯+ua−1Fpm are partitioned into aa distinct types. It is shown that for any unit ΛΛ of Type kk, a unit λλ of Type k∗k∗ can be constructed, such that the class of λλ-constacyclic of length psps of Type k∗k∗ codes is one-to-one correspondent to the class of ΛΛ-constacyclic codes of the same length of Type kk via a ring isomorphism. The units of RaRa of the form Λ=Λ0+uΛ1+⋯+ua−1Λa−1Λ=Λ0+uΛ1+⋯+ua−1Λa−1, where Λ0,Λ1,…,Λa−1∈FpmΛ0,Λ1,…,Λa−1∈Fpm, Λ0≠0,Λ1≠0, are considered in detail. The structure, duals, Hamming and homogeneous distances of ΛΛ-constacyclic codes of length psps over RaRa are established. It is shown that self-dual ΛΛ-constacyclic codes of length psps over RaRa exist if and only if aa is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both αα- and ββ-constacyclic over RaRa for different units αα, ββ.