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

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.

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