The work was published in:
Mat. Zametki 68 (2000), no. 4, pp. 483-503;

English translation: Math. Notes. 68 (2000), no. 4.

Arestov V.V. Babenko A.G.

A B S T R A C T

This work devote to known problem about maximal cardinality
(*s*) of spherical *s*-code
(- 1*s* < 1) in *m*-dimensional
Euclidean space
^{m}, *m*2; more precisely, it is
considered the Delsarte's function *w*_{m}(*s*) which connected with
(*s*) by inequality:
(*s*)*w*_{m}(*s*). Solution of the
equation *w*_{m}(*s*) = *N* for *m* = 4 and *N* = 24, 25 is found. As
consequence, it is obtained that among arbitrary 25 (resp.
24) points located on unit sphere in
^{4} there exist
two points with the angular distance between them strictly less
than
60.5^{o} (resp.
61.41^{o}).

Bibliogr. 24 titles.

*Key words:* spherical codes, kissing numbers, Chebyshev
polynomials of the second kind.