Complete classification of (δ + αu2) -constacyclic codes of length pk over Fpm + uFpm + u2Fpm

Abstract

Let R be the finite chain ring Fpm[u]/〈u3〉, where p is a prime and m is a positive integer. In this study we completely determine the structure of (δ+αu2)-constacyclic codes of length pk over R, that is, ideals of the ring R[x]/〈xpk-(δ+αu2)〉, where δ and α are nonzero elements in Fpm. We show that when p is odd, there is no self-dual (δ+αu2)-constacyclic code of length pk over R and also in the case where p=2, self-dual codes exist when δ=1. We completely determine self-dual (1+αu2)-constacyclic codes of length 2k over F2m[u]/〈u3〉 and enumerate them. © 2015 Elsevier Inc. All rights reserved.