Repeated-root constacyclic codes of prime power length over [Formula presented] and their duals

Abstract

© 2016 Elsevier B.V. The units of the chain ring [formula presented] are partitioned into a distinct types. It is shown that for any unit Λ of Type k, a unit λ of Type k∗can be constructed, such that the class of λ-constacyclic of length psof Type k∗codes is one-to-one correspondent to the class of Λ-constacyclic codes of the same length of Type k via a ring isomorphism. The units of Raof the form Λ=Λ0+uΛ1+⋯+ua−1Λa−1, where Λ0,Λ1,…,Λa−1∈Fpm, Λ0≠0,Λ1≠0, are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ-constacyclic codes of length psover Raare established. It is shown that self-dual Λ-constacyclic codes of length psover Raexist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α- and β-constacyclic over Rafor different units α, β.