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.

Estimates of maximal value of angular code distance for 24 and 25 points on unit sphere in $ \mathbb {R}$4

A B S T R A C T

This work devote to known problem about maximal cardinality $ \tau_{m}^{}$(s) of spherical s-code (- 1$ \le$s < 1) in m-dimensional Euclidean space $ \mathbb {R}$m, m$ \ge$2; more precisely, it is considered the Delsarte's function wm(s) which connected with $ \tau_{m}^{}$(s) by inequality: $ \tau_{m}^{}$(s)$ \le$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 $ \mathbb {R}$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.