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

Let R be the finite chain ring F-pm[u]/< u(3)>, where p is a prime and m is a positive integer. In this study we completely determine the structure of (delta + alpha u(2))-constacyclic codes of length p(k) over R, that is, ideals of the ring R[x]/< x(pk) - (delta + alpha u(2))>, where delta and alpha are nonzero elements in F-pm. We show that when p is odd, there is no self-dual (delta + alpha u(2))-constacyclic code of length p(k) over R and also in the case where p = 2, self-dual codes exist when delta = 1. We completely determine self-dual (1 + alpha u(2))-constacyclic codes of length 2(k) over F-2m [u]/< u3 > and enumerate them. (C) 2015 Elsevier Inc. All rights reserved.