In this talk a new extension of known semidefinite and linear programming upper bounds for spherical codes will be presented and consider a version of this bound for distance graphs. The main result can be applied for the distance distribution of a spherical code, and it will be shown that this method can work effectively. In particular, I get a shorter solution to the kissing number problem in dimension 4. I will consider reasonable approaches for a solutions of two long standing open problems: the uniqueness of maximum kissing arrangements in 4 dimensions and the 24-cell conjecture. In a recent preprint by de Laat -- Leijenhorst -- de Muinck Keizer claimed a solution to the uniqueness problem. We will also discuss their approach.