Abstract
Quasi-cyclic codes of length mn over Z 4 are shown to be equivalent to A-submodules of A n, where A = Z 4[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.
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Supported by the National Natural Science Foundation of China (60603016)
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Pei, Jy., Zhang, Xj. Quaternary quasi-cyclic codes. Appl. Math. J. Chin. Univ. 23, 359–365 (2008). https://doi.org/10.1007/s11766-008-1521-1
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DOI: https://doi.org/10.1007/s11766-008-1521-1