Additive codes over Galois rings

Let S = GR(p(e), m) be a Galois ring of characteristic p(e) and cardinality p(em). An additive code over S of length n is a subgroup of S-n under addition. In this paper, we study additive codes over S. We introduce a correspondence between linear codes over Z(pe) and additive codes over S and we describe additive codes over S by the structure of linear codes over Z(pe). In particular, we find the generator matrix and the number of additive codes over S, and we determine some classes of MDR additive codes over S. Among other results, permutation equivalent additive codes and decomposable additive codes are described. Also we prove MacWilliams identity and Delsarte theorem for additive codes over S. (C) 2018 Published by Elsevier Inc.