English

Optimality and uniqueness of the (4,10,1/6) spherical code

Metric Geometry 2008-11-15 v2

Abstract

Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code, which consists of the midpoints of the edges of the regular simplex in dimension 4, is the unique (4,10,1/6) spherical code.

Keywords

Cite

@article{arxiv.0708.3947,
  title  = {Optimality and uniqueness of the (4,10,1/6) spherical code},
  author = {Christine Bachoc and Frank Vallentin},
  journal= {arXiv preprint arXiv:0708.3947},
  year   = {2008}
}

Comments

12 pages, (v2) several small changes and corrections suggested by referees, accepted in Journal of Combinatorial Theory, Series A

R2 v1 2026-06-21T09:11:48.979Z