Consta-Abelian polyadic codes

In this correspondence, the class of polyadic codes is generalized to the class of consta-Abelian polyadic codes, which, in particular, includes the class of constacyclic polyadic codes. Properties such as the equivalence of polyadic codes and the mth-root lower bound for the minimum weight of a subcode of certain types of polyadic codes are preserved in the consta-Abelian case. Sufficient conditions for the existence of this class of codes are established. For the special case of constacyclic codes, the characterization of negacyclic self-dual codes of length coprime to the characteristic of the field in terms of negacyclic duadic codes is also given