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

In this paper, we study a relative two-weight $$\mathbb{Z}$_2 $\mathbb{Z}$_4$-additivecodes\mathrm{.}ItisshownthattheGrayimageofatwo-distance$$\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.