On extremal double circulant self-dual codes of lengths $90$-$96$

TL;DR

This paper classifies extremal double circulant self-dual codes of lengths 90 to 96, expanding known classifications and analyzing neighbor relationships to understand their structure and limitations.

Contribution

It provides the first classification of extremal double circulant self-dual codes for lengths 90, 92, 94, and 96, and examines neighbor properties of specific codes.

Findings

Classified extremal double circulant self-dual codes for lengths 90, 92, 94, 96

Identified that no extremal neighbor exists for certain codes at lengths 90 and 96

Determined limitations on self-dual neighbors with high minimum weight

Abstract

A classification of extremal double circulant self-dual codes of lengths up to $88$ is known. We give a classification of extremal double circulant self-dual codes of lengths $90,92,94$ and $96$. We also classify double circulant self-dual codes with parameters $[90,45,14]$ and $[96,48,16]$. In addition, we demonstrate that no double circulant self-dual $[90,45,14]$ code has an extremal self-dual neighbor, and no double circulant self-dual $[96,45,16]$ code has a self-dual neighbor with minimum weight at least $18$.