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

TL;DR

This paper investigates the structure and properties of relative two-weight $ ext{Z}_2 ext{Z}_4$-additive codes, showing their Gray images form binary two-distance codes and analyzing their automorphism groups.

Contribution

It characterizes the structure of relative two-weight $ ext{Z}_2 ext{Z}_4$-additive codes and their Gray images, and explores their permutation automorphism groups.

Findings

Gray image of a two-distance $ ext{Z}_2 ext{Z}_4$-additive code is a binary two-distance code.

Gray image of a relative two-weight $ ext{Z}_2 ext{Z}_4$-additive code with nontrivial binary part is a linear binary relative two-weight code.

The structure and automorphism groups of these codes are described.

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.