Counting Z2Z4-Additive Codes

Abstract

It is well known that the subsets of the Hamming scheme, with an abelian group structure, have been characterized by Delsarte as what is now known as Z(2)Z(4) codes. Z(2)Z(4)-additive codes give rise to Z(2)Z(4)-linear codes via a Gray map which are propelinear binary codes. In this paper, we define free Z(2)Z(4)-additive codes and count their number. We then count the number of arbitrary Z(2)Z(4)-additive codes of type (alpha, beta; gamma, delta; kappa).