New upper bounds for kissing numbers from semidefinite programming

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

Abstract: Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions. In particular our computations give the (known) values for the cases n = 3, 4, 8, 24.

Keywords: spherical codes, kissing number, semidefinite programming, Delsarte's method

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Combinatorial Optimization

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Entry Submitted: 08/16/2006
Entry Accepted: 08/16/2006
Entry Last Modified: 10/17/2006

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