Enumeration and construction of additive cyclic codes over Galois rings

Let R = GR(p, l) be a Galois ring of characteristic p and cardinality pεl, where p and l are prime integers. First, we give a canonical form decomposition for additive cyclic codes over R. This decomposition is used to construct additive cyclic codes and count the number of such codes, respectively. Thenwe give the trace dual code for each additive cyclic code over R from its canonical form decomposition and linear codes of length l over some extension Galois rings of Zpε . © 2015 Elsevier B.V. All rights reserved.