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 (- 1s < 1) in m-dimensional Euclidean space m, m2; 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.