Spherical Codes Linear Programming Bounds Distance Distribution
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 21, No 3, (1995), 231p-238p
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.