Generalized negacyclic codes over finite fields

Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice algebraic structures, wide applications and links with other mathematical objects. In this paper, a generalization of negacyclic codes is introduced and studied. Algebraic structures of such codes are given though cyclotomic classes of abelian groups and ideals in twisted group algebras. Recursive constructions and enumerations of such codes are presented. Characterizations of self-dual generalized negacyclic codes and complementary dual generalized negacyclic codes are given as well as their enumerations.