Improved upper bound on A(18,8)

TL;DR

This paper refines the semidefinite programming bounds for binary codes, establishing a new upper limit of 70 for the maximum size of a code with length 18 and minimum distance 8.

Contribution

It introduces a sharper semidefinite programming bound that improves the known upper limit for A(18,8).

Findings

A(18,8) ≤ 70, improving previous bounds.

Refinement of semidefinite programming techniques.

Enhanced bounds for binary code parameters.

Abstract

For nonnegative integers $n$ and $d$, let $A(n,d)$ be the maximum cardinality of a binary code of length $n$ and minimum distance at least $d$. We consider a slight sharpening of the semidefinite programming bound of Gijswijt, Mittelmann and Schrijver, and obtain that $A(18,8)\leq 70$.