Paper Title
A Semidefinite Programming Approach to the Spherical Codes Problem

Abstract
A spherical code is said to be an (n, N, γ)-code if it has dimension n, cardinality (size) N and a maximum cosine γ. It means that the dot product of unit vectors from the originto any two points on the unit sphere is less than or equal to γ. If each point onthe unit sphere is treated as an electron, one approach to this spherical code problem is to define an electrostatic energy of electrons and to optimize for their minimum values. A configuration with minimum energy corresponds to a useful spherical code, but may not be the global minimum solution. Thus, minimizing the energy function does not always resulted in a smallest γ for a set of N and n. A global solution for the spherical code problem for most of parameters (n,N)is unknown, especially for spherical codes in higher dimension. In this paper, a semidefinite programming approach for obtaining spherical codes is proposed.By running simulation with these algorithms, configurations for many of the best known spherical codes found in literature were obtained. Keywords - Spherical Code, Optimization, Sphere, Semidefinite Programing , Dot Product