English

Improved upper bound on A(18,8)

Combinatorics 2017-03-06 v2 Optimization and Control

Abstract

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

Keywords

Cite

@article{arxiv.1612.02178,
  title  = {Improved upper bound on A(18,8)},
  author = {Sven Polak},
  journal= {arXiv preprint arXiv:1612.02178},
  year   = {2017}
}

Comments

This paper has been withdrawn by the author, since the result turned out to be dated.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

R2 v1 2026-06-22T17:15:58.966Z