Journal of Statistical Physics, Vol. 71, Nos. 1/2, 1993. p. 327-339.
Hadamard theory is shown to play an important role in the generation of Boolean decision functions, a fundamental tool in the field of artificial neural network design. Based on a group-theoretic introduction of a complete set of Hadamard vectors, whose matrices are of the order of a power of two, we classify subsets according to the degree of their linear dependence. We show in the thermodynamic limit that essentially the whole Hadamard space is occupied by representatives with defect not exceeding two or three.