On the algebraic structure of quasi group codes

TL;DR

This paper provides an algebraic framework for quasi group codes, a class of linear codes with permutation symmetries, enabling their construction from ring-based codes and exploring their self-duality properties.

Contribution

It introduces an intrinsic algebraic description of quasi group codes, connecting them with codes over rings and analyzing their self-duality.

Findings

Quasi group codes can be constructed from codes over rings.

An algebraic and concatenated structure description of these codes is provided.

Conditions for self-duality of quasi group codes are investigated.

Abstract

In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms which acts freely on the set of coordinates. An algebraic description, including the concatenated structure, of such codes is presented. This allows to construct quasi group codes from codes over rings, and vice versa. The last part of the paper is dedicated to the investigation of self-duality of quasi group codes.