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Title: New Upper Bounds for Some Spherical Codes
Authors: Boyvalenkov, Peter
Kazakov, Peter
Keywords: Spherical Codes
Linear Programming Bounds
Distance Distribution
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 3, (1995), 231p-238p
Abstract: 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.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 3

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