155 citations · 475 across the 22 of their papers we have counts for
4 papers · 1 filter
Polarization of lattices: Stable cold spots and spherical designs
Christine Bachoc, Philippe Moustrou, Frank Vallentin +1
We consider the problem of finding the minimum of inhomogeneous Gaussian lattice sums: Given a lattice and a positive constant , the goal is to find t…
Optimality and uniqueness of the (4,10,1/6) spherical code
Christine Bachoc, Frank Vallentin
Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6…
Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
Christine Bachoc, Frank Vallentin
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-si…
New upper bounds for kissing numbers from semidefinite programming
Christine Bachoc, Frank Vallentin
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…