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Automatic Control and Computer Sciences

, Volume 49, Issue 3, pp 153–158 | Cite as

On two predictors of calculable chains of quasi-orthogonal matrices

  • N. A. Balonin
  • A. A. Vostrikov
  • M. B. Sergeev
Article

Abstract

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.

Keywords

quasi-orthogonal matrices Hadamard matrices Belevitch matrices Mersenne matrices Euler matrices Seidel matrices three-level Legendre symbols two-circulant matrices 

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Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  • N. A. Balonin
    • 1
  • A. A. Vostrikov
    • 1
  • M. B. Sergeev
    • 2
  1. 1.Saint Petersburg State University of Aerospace InstrumentationSt. PetersburgRussia
  2. 2.Saint Petersburg National Research University of Information Technologies, Mechanics and OpticsSt. PetersburgRussia

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