# On checkable codes in group algebras

## TL;DR

This paper classifies group algebras over finite groups where all right ideals are right annihilators of principal left ideals, extending the concept of code-checkable group algebras beyond abelian groups and discussing their optimality.

## Contribution

It provides a classification of code-checkable group algebras for all finite groups based on their structure, generalizing previous results limited to abelian groups.

## Key findings

- Complete classification of code-checkable group algebras for finite groups
- Discussion on the optimality of checkable codes
- Asymptotic properties of these codes

## Abstract

We classify, in terms of the structure of the finite group G, all group algebras KG for which all right ideals are right annihilators of principal left ideals. This means in the language of coding theory that we classify code-checkable group algebras KG which have been considered so far only for abelian groups G. Optimality of checkable codes and asymptotic results are discussed.