# New doubly even self-dual codes having minimum weight 20

## TL;DR

This paper constructs new doubly even self-dual codes with minimum weight 20 for lengths 112, 120, and 128, revealing the existence of multiple inequivalent extremal codes at length 112.

## Contribution

It introduces new extremal doubly even self-dual codes of specific lengths, expanding the known classifications.

## Key findings

- Existence of at least three inequivalent extremal codes of length 112.
- Construction of new codes with minimum weight 20 for lengths 120 and 128.
- Enhanced understanding of the structure of self-dual codes.

## Abstract

In this note, we construct new doubly even self-dual codes having minimum weight $20$ for lengths $112$, $120$ and $128$. This implies that there are at least three inequivalent extremal doubly even self-dual codes of length $112$.