Volume 19, No 1, 2012, P. 3-16

UDC 519.8
A. Yu. Vasil’eva
On reconstructive sets of vertices in the Boolean cube

Abstract:
The notion of a reconstructive set of the Boolean cube is introduced in terms of Fourier transform. The characterization of linear reconstructive sets is obtained. Necessary and sufficient conditions of the reconstructivity of a sphere are established. Sufficient conditions of the reconstructivity of two concentric spheres are found.
Bibliogr. 9.

Keywords: Fourier transform, reconstructive set, linear subspace, Krawtchouk polynomial, Johnson scheme.

Vasil’eva Anastasia Yur’evna ¹
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: vasilan@math.nsc.ru