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

doi:10.1016/j.jcta.2008.05.001

Journal of Combinatorial Theory, Series A

Volume 116, Issue 1, January 2009, Pages 195-204

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Abstract

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.

Keywords

Linear programming

Semidefinite programming

Spherical codes

Spherical designs

Petersen graph

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¹: Supported by the Netherlands Organization for Scientific Research under grant NWO 639.032.203 and by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-2.

Journal of Combinatorial Theory, Series A

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

Abstract

Keywords

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