Complete classification of repeated-root [formula omitted]-constacyclic codes of prime power length over [formula omitted

Abstract

Let R=Fpm[u]∕〈u3〉 be the finite commutative chain ring with unity, where p is a prime, m is a positive integer and Fpm is a finite field with pm elements. In this study, we investigate σ-constacyclic codes of length ps over R, that is, ideals of the ring R[x]∕〈xps−σ〉, where σ is a nonzero element of the field Fpm. First, we classify all cyclic codes of length ps over R and obtain the number of codewords in each type of those cyclic codes. Furthermore, by using the ring isomorphism we completely determine the structure of σ-constacyclic codes of length ps over R.