Complementary dual abelian codes in group algebras of some finite abelian groups

Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

^* e-mail: sjitman@gmail.com

Abstract

Linear complementary dual codes have become an interesting sub-family of linear codes over finite fields since they can be practically applied in various fields such as cryptography and quantum error-correction. Recently, properties of complementary dual abelian codes were established in group algebras of arbitrary finite abelian groups. However, the enumeration formulas were given mostly based on number-theoretical characteristic functions. In this article, complementary dual abelian codes determined by some finite abelian groups are revisited. Specifically, the characterization of cyclotomic classes of an abelian group and the enumeration of complementary dual abelian codes are presented, where the group is a finite abelian p-group, a finite abelian 2-group, and a product of a finite abelian p-group and a finite abelian 2-group for some odd prime number p different from the characteristic of the alphabet filed. The enumeration formula for such complementary dual codes is given explicitly in a more precise form without characteristic functions. Some illustrative examples are given as well.