Let S=GR(pe, m)be a Galois ring of characteristic peand cardinality pem. An additive code over Sof length nis a subgroup of Snunder addition. In this paper, we study additive codes over S. We introduce a correspondence between linear codes over Zpeand additive codes over Sand we describe additive codes over Sby the structure of linear codes over Zpe. In particular, we find the generator matrix and the number of additive codes over S, and we determine some classes of MDRadditive 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.
