Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of A^n, where A = Z4[x]/（x^m - 1）. In the case of m being odd, all quasi-cyclic codes are shown to be decomposable into the direct s...Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of A^n, where A = Z4[x]/（x^m - 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.展开更多
基金the National Natural Science Foundation of China (60603016)
文摘Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of A^n, where A = Z4[x]/（x^m - 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.
