Enumeration and construction of additive cyclic codes over Galois rings

Let R = GR ( p ? , l ) be a Galois ring of characteristic p ? and cardinality p ? l , 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. Then we 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 Z p ? .

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