# Group codes over fields are asymptotically good

## TL;DR

This paper proves that group codes over finite fields of any characteristic are asymptotically good, extending previous results from binary fields to all finite fields.

## Contribution

It establishes the asymptotic goodness of group codes over arbitrary finite fields, generalizing prior work limited to binary fields.

## Key findings

- Group codes over finite fields are asymptotically good.
- The result extends to fields of any characteristic.
- Supports the potential of group codes in coding theory applications.

## Abstract

Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following ideas of Bazzi and Mitter on group codes over the binary field, we prove that group codes over finite fields of any characteristic are asymptotically good.