The structure of Z2Z2s-additive cyclic codes

Abstract

Z(2)Z(2)s-additive codes for any integer s > 1 are considered as codes over mixed alphabets. They are a generalization of binary linear codes and linear codes over Z(2)s. In this paper, we are interested in studying Z(2)Z(2)s-additive cyclic codes. We will give the generator polynomials of these codes. We will also give the minimal spanning sets for these codes. We will define separable Z(2)Z(2)s-additive codes and provide conditions on the generator polynomials for a Z(2)Z(2)s-additive cyclic code to be separable. Finally, we present some examples of optimal parameter binary codes obtained as images of Z2Z8-additive cyclic codes.