On Kissing Numbers in Dimensions 32 to 128
نویسندگان
چکیده
An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.
منابع مشابه
Improved Delsarte bounds for spherical codes in small dimensions
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.
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The “kissing number problem” asks for the maximal number of white spheres that can touch a black sphere of the same size in n-dimensional space. The answers in dimensions one, two and three are classical, but the answers in dimensions eight and twenty-four were a big surprise in 1979, based on an extremely elegant method initiated by Philippe Delsarte in the early seventies, which concerns ineq...
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In this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings ...
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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...
متن کامل1 3 M ay 1 99 4 Average kissing numbers for non - congruent sphere packings
(The appearance of the number of the beast in the lower bound is purely coincidental.) The supremal average kissing number k is defined in any dimension, as are kc, the supremal average kissing number for congruent ball packing, and ks, the maximal kissing number for a single ball surrounded by congruent balls with disjoint interiors. (Clearly, kc ≤ k and kc ≤ ks.) It is interesting that k is a...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 5 شماره
صفحات -
تاریخ انتشار 1998