Galois LCD codes over mixed alphabets

TL;DR

This paper characterizes Galois linear complementary dual codes over mixed alphabets from finite chain rings and explores their Gray images, expanding understanding of their structure and invariance properties.

Contribution

It provides a characterization of Galois LCD codes over mixed alphabets and analyzes their Gray images, introducing new insights into their structure and invariance.

Findings

Characterization of Galois LCD codes over mixed alphabets

Conditions for Galois invariance of these codes

Analysis of Gray images leading to new LCD codes

Abstract

We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[\theta]$-linear codes, where $p\in\{2; 3\}$ and $\theta\neq\theta^2=0$, that provides $\mathbb{F}_p$-linear complementary dual codes.