# New upper bounds for kissing numbers from semidefinite programming

@article{Bachoc2006NewUB, title={New upper bounds for kissing numbers from semidefinite programming}, author={Christine Bachoc and Frank Vallentin}, journal={Theoretical Computer Science}, year={2006} }

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 upper bounds for the kissing number in several dimensions. In particular our computations give the (known) values for the cases .

## 90 Citations

### Semidefinite programming bounds for spherical codes

- Computer Science2007 IEEE International Symposium on Information Theory
- 2007

This paper develops a new method to obtain upper bounds for spherical codes, based on semidefinite programming. With this method we improve the previous bounds for the kissing number in several…

### Bounds for codes by semidefinite programming

- Mathematics, Computer Science
- 2006

It is shown that using as variables power sums of distances, the upper bound problem for codes in two-point homogeneous spaces can be considered as a finite semidefinite programming problem.

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

- Computer Science, MathematicsEur. J. Comb.
- 2009

### SEMIDEFINITE PROGRAMMING BOUNDS FOR KISSING NUMBERS

- Mathematics
- 2018

The kissing number in n-dimensional Euclidean space is the maximal number of non-overlapping unit spheres which simultaneously can touch a central unit sphere. Bachoc and Vallentin developed a method…

### High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

- MathematicsExp. Math.
- 2010

High-accuracy calculations of upper bounds for the kissing number based on semidefinite programming are reported on, finding that there is no 16-dimensional periodic sphere packing with average theta series.

### Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry

- Computer Science
- 2018

This article exploits the symmetry present in the semidefinite programming bound to provide improved upper bounds for the kissing number for n = 9, …, 23.

### Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry

- Computer ScienceExp. Math.
- 2018

The symmetry present in the semidefinite programming bound of Bachoc and Vallentin (2008) is exploited to provide improved upper bounds for the kissing number for values of n = 9, \ldots, 23.

### An extension the semidefinite programming bound for spherical codes

- Computer Science, Mathematics
- 2019

In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result…

### Bounds for codes via semidefinite programming

- Mathematics, Computer Science2009 Information Theory and Applications Workshop
- 2009

Two extensions of Delsarte's method via semidefinite programming are considered and an extension of Schoenberg's theorem for multivariate Gegenbauer polynomials has been proved.

### Upper bounds for energies of spherical codes of given cardinality and separation

- Computer ScienceDes. Codes Cryptogr.
- 2020

A linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance is introduced using Hermite interpolation and polynomials are constructed.

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