On exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions

Abstract

We study the exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions. It is shown that the sufficient number of nodes for discretization with the minimal number of nodes is equal to $N$ or $N+1$ and depends on the dimension $N$. The connection with Hadamard matrices and the Hadamard conjecture is demonstrated.

6 pages