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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174087Linear 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 AMetric Geometry52C17, 90C22Optimality and uniqueness of the (4,10,1/6) spherical codetext