On the classification of binary self-dual [44,22,8] codes with an automorphism of order 3 or 7

TL;DR

This paper completes the classification of extremal binary self-dual [44,22,8] codes with automorphisms of order 3 or 7, advancing understanding of their structure and symmetry properties.

Contribution

It provides a complete classification of such codes with automorphisms of order 3 or 7, filling a gap in the existing literature.

Findings

All codes with automorphisms of order 3 are classified.

All codes with automorphisms of order 7 are classified.

The classification completes the understanding of extremal self-dual codes of length 44 with odd prime automorphisms.

Abstract

All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified. In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.