Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in R-4 / Arestov VV,Babenko AG // MATHEMATICAL NOTES. - 2000. - V. 68, l. 3-4. - P. 419-435.

ISSN/EISSN:

0001-4346 / нет данных

Type:

Article

Abstract:

The present paper is devoted to the well-known problem of determining the maximum number of elements pi (m)(s) of a spherical s-code (-1 less than or equal to s < 1) in Euclidean space R-m of dimension m 2; to be exact, here we consider the Delsarte function w(m)(s) related to tau (m)(s) via the inequality tau (m)(s) less than or equal to w(m)(s). In this paper, the solution of the equation w(m)(s) = N is obtained for m = 4 and N = 24, 25. As a consequence, we obtain the assertion that among any 25 (24) points on the unit sphere in the space R-4 there always exist two points with angular distance between them strictly less than 60.5 degrees (61.41 degrees).

Author keywords:

spherical code; spherical packings; kissing numbers; Delsarte function; Chebyshev polynomials of the second kind; Gegenbauer polynomials BOUNDS

DOI:

10.1007/BF02676721

Web of Science ID:

ISI:000165571900021

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	SEP-OCT
Publisher	CONSULTANTS BUREAU
Address	233 SPRING ST, NEW YORK, NY 10013 USA
Language	English
Keywords-Plus	BOUNDS
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Number-of-Cited-References	24
Usage-Count-Since-2013	1
Journal-ISO	Math. Notes
Doc-Delivery-Number	378EK