Title

Delsarte-Yudin LP Method and Universal Lower Bounds on Energy

Document Type

Presentation

Presentation Date

Spring 4-21-2015

Conference Name

2015 Workshop on Combinatorics and Applications at SJTU

Conference Location

Shanghai Jiao Tong University, Shanghai, China

Peer Review

Invited

Abstract

We derive universal lower bounds for the potential energy of spherical codes and codes in Hamming spaces, that are optimal in the framework of Delsarte's linear programming approach adapted for energy bounds by Yudin. 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.

Keywords

Spherical codes, potential energy, universally optimal configurations

Disciplines

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