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

Christine Bachoc(Christine.Bachocmath.u-bordeaux1.fr)
Frank Vallentin(f.vallentincwi.nl)

Abstract: Traditionally, optimality and uniqueness of an (n,N,t) spherical code is proved using linear programming bounds. However, this approach does not apply to the parameter (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code (which are the vertices of the 4-dimensional second hypersimplex or the midpoints of the edges of the regular simplex in dimension 4) is the unique (4,10,1/6) spherical code.

Keywords: linear programming bounds, semidefinite programming bounds, spherical codes, spherical designs, association schemes

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

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Entry Submitted: 08/29/2007
Entry Accepted: 08/29/2007
Entry Last Modified: 08/29/2007

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