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 w_m(s) which connected with $\tau_{m}^{}$(s) by inequality: $\tau_{m}^{}$(s)$\le$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 $\mathbb {R}$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.