Classification of 8-divisible binary linear codes with minimum distance 24

TL;DR

This paper classifies specific 8-divisible binary linear codes with minimum distance 24 and small length, and applies findings to codes related to nodal sextics with 65 double points.

Contribution

It provides a complete classification of certain 8-divisible binary codes and connects these codes to algebraic geometry problems involving nodal sextics.

Findings

Classification of all such codes for small lengths

Identification of codes related to nodal sextics with 65 double points

Potential applications in algebraic geometry and coding theory

Abstract

We classify 8-divisible binary linear codes with minimum distance 24 and small length. As an application we consider the codes associated to nodal sextics with 65 ordinary double points.