Good Codes From Dihedral Groups

TL;DR

This paper presents a straightforward method to construct codes using left ideals in group algebras of dihedral groups, demonstrating their potential to achieve optimal weights comparable to the best known codes of the same length.

Contribution

It introduces a novel construction of codes from dihedral group algebras, showing they can produce high-quality codes with optimal weights.

Findings

Codes with weights equal to the best known codes

Simple construction method from dihedral groups

Potential for high-performance coding applications

Abstract

We give a simple construction of codes from left ideals in group algebras of certain dihedral groups and give an example to show that they can produce codes with weights equal to those of the best known codes of the same length.