Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps

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

Abstract: In this paper we apply the semidefinite programming approach developed by the authors to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in particular get a new tight bound in dimension 8. Furthermore we show how to use the SDP framework to get analytic bounds.

Keywords: spherical caps, one-sided kissing number, orthogonal polynomials

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Combinatorial Optimization

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Entry Submitted: 10/30/2006
Entry Accepted: 10/30/2006
Entry Last Modified: 10/30/2006

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