A complete classification of doubly even self-dual codes of length 40

TL;DR

This paper provides a comprehensive classification of binary doubly even self-dual codes of length 40, and as a result, also classifies extremal self-dual codes of length 38, advancing understanding in coding theory.

Contribution

It offers the first complete classification of doubly even self-dual codes of length 40, filling a gap in the literature and enabling further research in the field.

Findings

Complete list of doubly even self-dual codes of length 40

Classification of extremal self-dual codes of length 38

Enhanced understanding of code structures and properties

Abstract

A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.