Three results on twisted $G-$codes and skew twisted $G-$codes

TL;DR

This paper advances the understanding of twisted G-codes by establishing conditions for checkability, classifying certain ideals as abelian group codes, and providing bounds on their dimension and distance.

Contribution

It solves an open problem on checkability, generalizes a classification of ideals, and derives bounds for twisted G-codes, expanding theoretical knowledge in coding theory.

Findings

Twisted skew group codes are checkable under specific conditions.

All ideals of dimension 3 are abelian group codes.

A bound on the dimension and distance of twisted group codes is established.

Abstract

In this paper we solve an open question formulated in the original paper of twisted skew group codes regarding when a twisted skew group code is checkable. Also, we prove that all ideals of dimension 3 over a twisted group algebra are abelian group codes, generalising another previous result over group algebras. Finally, we prove a bound on the dimension and distance of a twisted group code, as well as when such bound is reached.