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

DOI10.1016/j.ejc.2008.07.017zbMath1171.94378arXivmath/0610856OpenAlexW2140695699MaRDI QIDQ1011505

Frank Vallentin, Christine Bachoc

Publication date: 8 April 2009

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610856

zbMATH Keywords

bounds on codessemidefinite programmingkissing numbersmultivariable orthogonal polynomialscodes in spherical caps

Mathematics Subject Classification ID

Related Items (9)

Three-point bounds for energy minimization ⋮ Optimal arrangements of classical and quantum states with limited purity ⋮ A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4 ⋮ Towards a proof of the 24-cell conjecture ⋮ Invariant Semidefinite Programs ⋮ Optimality and uniqueness of the \((4,10,1/6)\) spherical code ⋮ Bounds for codes by semidefinite programming ⋮ Exact Semidefinite Programming Bounds for Packing Problems ⋮ A survey on spherical designs and algebraic combinatorics on spheres

Uses Software

• CSDP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounds for codes by semidefinite programming
• Codes in spherical caps
• Optimal arrangements in packing congruent balls in a spherical container
• The one-sided kissing number in four dimension
• Ten-neighbour packing of equal balls
• Spherical codes and designs
• New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
• Linear programming bounds for codes in grassmannian spaces
• New upper bounds for kissing numbers from semidefinite programming
• Uniqueness of Certain Spherical Codes
• CSDP, A C library for semidefinite programming

This page was built for publication: Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps