The work was published in:
Mat. Zametki 68 (2000), no. 4, pp. 483-503;
English translation: Math. Notes. 68 (2000), no. 4.
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 wm(s) which connected with
(s) by inequality:
(s)
wm(s). Solution of the
equation wm(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
60.5o (resp.
61.41o).
Bibliogr. 24 titles.
Key words: spherical codes, kissing numbers, Chebyshev
polynomials of the second kind.