We apply the semidefinite programming approach developed in arxiv:math.MG/0608426 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.
Additional Metadata
Keywords spherical codes, spherical caps, one-sided kissing number, semidefinite programming, orthogonal polynomials
MSC dimensions (msc 52C17), Semidefinite programming (msc 90C22)
THEME Logistics (theme 3)
Publisher Academic Press
Journal European Journal of Combinatorics
Citation
Bachoc, C, & Vallentin, F. (2009). Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps. European Journal of Combinatorics, 30, 625–637.