Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
European Journal of Combinatorics , Volume 30 p. 625- 637
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.
|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)|
|Journal||European Journal of Combinatorics|
Bachoc, C, & Vallentin, F. (2009). Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps. European Journal of Combinatorics, 30, 625–637.