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On two predictors of calculable chains of quasi-orthogonal matrices

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The general definition of quasi-orthogonal matrices, the definition of low-level matrices, and partial definitions of quasi-orthogonal Mersenne and Euler matrices are considered. New quasi-orthogonal symmetric Seidel matrices that exist on odd orders and three-level Legendre symbols used to calculate elements of these matrices are defined. A method to calculate Euler matrices via Mersenne matrices is given. A relation between asymmetric and symmetric odd-order Mersenne and Seidel matrices is shown to exist. A new, modified Sylvester method for calculating Euler matrices using symmetric circulant Seidel matrices is proposed.

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Correspondence to N. A. Balonin.

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Original Russian Text © N.A. Balonin, A.A. Vostrikov, M.B. Sergeev, 2015, published in Avtomatika i Vychislitel’naya Tekhnika, 2015, No. 3, pp. 42–48.

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Balonin, N.A., Vostrikov, A.A. & Sergeev, M.B. On two predictors of calculable chains of quasi-orthogonal matrices. Aut. Control Comp. Sci. 49, 153–158 (2015).

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