Binary quasi-cyclic codes of index 2 and skew polynomial rings

Abstract We present a study of the factorization of the polynomial X m − 1 in M 2 ( F 2 ) [ X ] and we determine the period of any reversible polynomial of this polynomial ring by using skew polynomial rings. These results are applied to the construction of the class of quasi-cyclic codes Ω ( P ) introduced by Cayrel et al. Furthermore, we present a new construction of the self dual subclass.

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