Add to ORKGWe 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
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
In the present paper we study the minimization of energy integrals on the sphere with a focus on an ...
Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive unive...
We derive universal lower bounds for the potential energy of spherical codes, that are optimal in th...
We derive and investigate lower bounds for the potential energy of finite spherical point sets (sphe...
We derive universal lower bounds for the potential energy of spherical codes and codes in Hamming sp...
Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive unive...
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potenti...
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, ...
Abstract. Three-point semidefinite programming bounds are one of the most powerful known tools for b...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
For many extremal configurations of points on a sphere, the linear programming approach can be used ...
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
In the present paper we study the minimization of energy integrals on the sphere with a focus on an ...
Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive unive...
We derive universal lower bounds for the potential energy of spherical codes, that are optimal in th...
We derive and investigate lower bounds for the potential energy of finite spherical point sets (sphe...
We derive universal lower bounds for the potential energy of spherical codes and codes in Hamming sp...
Based upon the works of Delsarte-Goethals-Seidel, Levenshtein, Yudin, and Cohn-Kumar we derive unive...
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potenti...
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, ...
Abstract. Three-point semidefinite programming bounds are one of the most powerful known tools for b...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
We provide new answers about the distribution of mass on spheres so as to minimize energies of pairw...
For many extremal configurations of points on a sphere, the linear programming approach can be used ...
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
A spherical code with parameter $(n, N,\gamma)$ is a set of N points on the unit sphere in $n$ dimen...
In the present paper we study the minimization of energy integrals on the sphere with a focus on an ...