# On Z2Z4-additive complementary dual codes and related LCD codes

## TL;DR

This paper introduces a new class of additive codes over mixed binary and quaternary alphabets, exploring their structure and constructing binary LCD codes via the Gray map, extending the concept of LCD codes beyond linear codes.

## Contribution

It defines and analyzes Z2Z4-additive LCD codes, a novel class of additive codes over mixed alphabets, and provides methods to construct binary LCD codes from them.

## Key findings

- Defined Z2Z4-additive LCD codes and studied their structure.
- Used Gray map to construct binary LCD codes from these additive codes.
- Extended LCD code concepts to additive, non-linear codes over mixed alphabets.

## Abstract

Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases.