Document Type

Presentation

Presentation Date

Summer 8-18-2015

Conference Name

10th Summer School in Potential Theory

Conference Location

Budapest, Hungary

Peer Review

Invited

Abstract

We derive universal lower bounds for the potential energy of spherical codes, that are optimal in the framework of Delsarte-Yudin linear programming method. Our bounds are universal in the sense of both Levenshtein and Cohn-Kumar; i.e., they are valid for any choice of dimension and code cardinality and they apply to any absolutely monotone potential. We further discuss a characterization on when the lower bounds are LP-optimal, that is they are the best possible in terms of the linear programming approach. Finally, we present the analogous results for codes in projective spaces.

Keywords

potential energy, spherical codes, universal configurations

Disciplines

Analysis | Discrete Mathematics and Combinatorics | Other Physical Sciences and Mathematics

Share

COinS