Pseudo-Hadamard matrices of the first generation and an algorithm for producing them

Hadamard matrices in {0, 1} presentation are square m × m matrices whose entries are zeros and ones and whose rows considered as vectors in Rm produce the Gram matrix of a special form with respect to the standard scalar product in R m. The concept of Hadamard matrices is extended in the present paper. As a result pseudo-Hadamard matrices of the first generation are defined and investigated. An algorithm for generating these pseudo-Hadamard matrices is designed and is used for testing some conjectures.