The Structure of Z2Z2s-Additive Codes: Bounds on the Minimum Distance

Abstract

Z(2)Z(4)-additive codes, as a special class of abelian codes, have found a very welcoming place in the recent studies of algebraic coding theory. This family in one hand is similar to binary codes on the other hand is similar to quaternary codes. The structure of Z(2)Z(4)-additive codes and their duals has been determined lately. In this study we investigate the algebraic structure of Z(2)Z(2)s-additive codes which are a natural generalization of Z(2)Z(4)-additive codes. We present the standard form of the generator and parity-check matrices of the Z(2)Z(2)s-additive codes. Also, we give two bounds on the minimum distance of Z(2)Z(2)s-additive codes and compare them.