Geodesic
New Upper Bounds for Some Spherical Codes
Serdica Mathematical Journal, Tome 21 (1995) no. 3, pp. 231-238.

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The maximal cardinality of a code W on the unit sphere in n dimensions 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 Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.
Keywords: Spherical Codes, Linear Programming Bounds, Distance Distribution 
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Boyvalenkov, Peter; Kazakov, Peter. New Upper Bounds for Some Spherical Codes. Serdica Mathematical Journal, Tome 21 (1995) no. 3, pp. 231-238. http://geodesic.mathdoc.fr/item/SMJ2_1995_21_3_a4/