Relative two-weight ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive Codes

Abstract

In this paper, we study a relative two-weight ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive codes. It is shown that the Gray image of a two-distance ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code is a binary two-distance code and that the Gray image of a relative two-weight ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive codes are described. Finally, we discussed permutation automorphism group of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive codes.