Quaternary quasi-cyclic codes

Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of An,where A = Z4 x /(xm -1).In the case of m being odd,all quasi-cyclic codes are shown to be decomposable into the direct sum of a fixed number of cyclic irreducible A-submodules.Finally the distinct quasi-cyclic codes as well as some specific subclasses are enumerated.