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

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

2007-08-29

arxiv.org/abs/0708.3947v2

J. Comb. Theory Ser. A 116 (2009), 195-204

Mathematics

Metric Geometry

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

Scientific paper

10.1016/j.jcta.2008.05.001

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.

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