Quasi-cyclic codes over Zps

The quasi-cyclic codes of length mn over R=Zps were studied, where p is a prime and s is an arbitrary positive integer. By exploring the structure, the quasi-cyclic codes of length mn over R were shown to be equivalent to A-submodules of An, where A=R［x］/(xm－1). Then the case was studied in which quasi-cyclic codes over R can be decomposed into a direct sum of a fixed number of irreducible cyclic submodules when gcd(m,p)=1.