Enumeration and construction of additive cyclic codes over Galois rings

Let R=GR(pϵ,l) be a Galois ring of characteristic pϵpϵ and cardinality pϵlpϵl, where pp and ll are prime integers. First, we give a canonical form decomposition for additive cyclic codes over RR. This decomposition is used to construct additive cyclic codes and count the number of such codes, respectively. Then we give the trace dual code for each additive cyclic code over RR from its canonical form decomposition and linear codes of length ll over some extension Galois rings of ZpϵZpϵ.