Semidefinite programming bounds for distance distribution of spherical codes

TL;DR

This paper extends semidefinite and linear programming bounds to improve estimates of the distance distribution in spherical codes, leading to a shorter solution to the kissing number problem in four dimensions.

Contribution

It introduces an extended method for bounding spherical codes using semidefinite programming, enhancing previous bounds and solving the kissing number problem more efficiently in dimension 4.

Findings

Extended bounds improve estimates for spherical code distributions

Achieved a shorter proof for the kissing number in 4D

Demonstrated effectiveness of the new method in practical problems

Abstract

We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular, we get a shorter solution to the kissing number problem in dimension 4.