Optimality and uniqueness of the (4,10,1/6) spherical code
arXiv:0708.3947 · doi:10.1016/j.jcta.2008.05.001
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.
12 pages, (v2) several small changes and corrections suggested by referees, accepted in Journal of Combinatorial Theory, Series A