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

05/19/2021

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by   Ruslan Sharipov, et al.

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Hadamard matrices in {0,1} presentation are square m× m matrices whose entries are zeros and ones and whose rows considered as vectors in R^m 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.