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

摘要

Linear programming bounds provide ail 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. (C) 2008 Elsevier Inc. All rights reserved.