  In the present paper, we examine Ising systems on d-dimensional hypercube
lattices and solve an inverse problem where we have to determine interaction
constants of an Ising connection matrix when we know a spectrum of it
eigenvalues. In addition, we define restrictions allowing a random number
sequence to be a connection matrix spectrum. We use the previously obtained
analytical expressions for the eigenvalues of Ising connection matrices
accounting for an arbitrary long-range interaction and supposing periodic
boundary conditions.
