arXiv:0708.3947 Abstract | arXiv Analytics

arXiv:0708.3947 [math.MG]Abstract References Reviews Resources

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

Published 2007-08-29, updated 2008-05-14Version 2

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.

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

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

DOI: 10.1016/j.jcta.2008.05.001

Categories: math.MG

Subjects: 52C17, 90C22

Keywords: spherical code, optimality, uniqueness, semidefinite programming bounds, petersen code

Tags: journal article

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