Improved Delsarte bounds for spherical codes in small dimensions
نویسنده
چکیده
We present an extension of the Delsarte linear programming method for spherical codes. For several dimensions it yields improved upper bounds including some new bounds on kissing numbers. Musin’s recent work on kissing numbers in dimensions three and four can be formulated in our framework.
منابع مشابه
Improved Delsarte Bounds via Extension of the Function Space
A spherical (n,N, α)-code is a set {x1, . . . ,xN} of unit vectors in R such that the pairwise angular distance betweeen the vectors is at least α. One tries to find codes which maximize N or α if the other two values are fixed. The kissing number problem asks for the maximum number k(n) of nonoverlapping unit balls touching a central unit ball in n-space. This corresponds to the special case o...
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We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...
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I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a nonnegative linear combination of Gegenbauer polynomials. This fact play a crucial role in Delsarte’s method for finding bounds for the density of sphere packings on spheres and Euclidean spaces. One of the most excited applications of Delsarte’s method is a solution of the kissing ...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 114 شماره
صفحات -
تاریخ انتشار 2007