Volume 19, No 1, 2012, P. 3-16
A. Yu. Vasil’eva
On reconstructive sets of vertices in the Boolean cube
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.
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