Improved upper bound on A(18,8)

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 $A(18,8)\le 70$.

This paper has been withdrawn by the author, since the result turned out to be dated. Östergard obtained the more strict bound $A(18,8)\le 68$, which appeared in Applicable Algebra in Engineering, Communication and Computing, Volume 24,Issue 3, pp 197-200, 2013