New upper bounds for some spherical codes

The maximal cardinality of a code W on the unit sphere in n dimen- sions with (x,y) ≤ s whenever x,y ∈ W, x 6 y, is denoted by A(n,s). We use two methods for obtaining new upper bounds on A(n,s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Lev- enshtein (11, 12). Also we investigate the possibilities for attaining the Levenshtein bounds (11, 12). In such cases we find the distance distributions of the correspond- ing feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.