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REGULAR HADAMARD MATRIX OF ORDER 196 AND SIMILAR MATRICES

Purpose: This note discusses two level quasi-orthogonal matrices which were first highlighted by J. J. Sylvester; Hadamard matrices, symmetric conference matrices, and weighing matrices are the best known of these matrices with entries from the unit disk. The goal of this note is to develop a theory of such matrices based on preliminary research results. Methods: Our new regular Hadamard matrix constructed for order 196, suggests a source of ideas to construct regular Hadamard matrices of orders n = 1 + p  q = 1 + p  (1 + 2m), where p, q are twin odd integer (q – p = 2); m = (q – 1)/2, prime, order of inner blocks. Results: We present a new method aimed to give regular Hadamard matrix of order 196 and similar matrices. Such kinds of regular Hadamard matrix of order 36 were done by Jennifer Seberry (1969), that inspired to find matrices of orders 4k2, k integer, 36, 100, 196, …, 1444 and many others. We apply this result to the family of regular matrices obtaining a new infinite family of Cretan matrices with orders 4t + 1, t an integer, 37, 101, 197, …, 1445, etc. Practical relevance: Web addresses are given for other illustrations and other matrices with similar properties. Algorithms to construct regular matrices have been implemented in developing software of the research program-complex. doi:10.15217/issn1684-8853.2015.1.2

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ТЕОРЕТИЧЕСКАЯ И ПРИКЛАДНАЯ МАТЕМАТИКА UDC 004.438 doi:10.15217/issn1684-8853.2015.1.2 REGULAR HADAMARD MATRIX OF ORDER 196 AND SIMILAR MATRICES N. A. Balonina, Dr. Sc., Tech., Professor, korbendfs@mail.ru M. B. Sergeeva, Dr. Sc., Tech., Professor, mbse@mail.ru aSaint-Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, Saint-Petersburg, Russian Federation Purpose: This note discusses two level quasi-orthogonal matrices which were first highlighted by J. J. Sylvester; Hadamard matrices, symmetric conference matrices, and weighing matrices are the best known of these matrices with entries from the unit disk. <...> The goal of this note is to develop a theory of such matrices based on preliminary research results. <...> Results: We present a new method aimed to give regular Hadamard matrix of order 196 and similar matrices. <...> Practical relevance: Web addresses are given for other illustrations and other matrices with similar properties. <...> Algorithms to construct regular matrices have been implemented in developing software of the research program-complex. <...> Keywords — Quasi-Orthogonal Matrices, Hadamard Matrices, Regular Hadamard Matrices, Cretan Matrices, Legendre We present a new method aimed to give regular Hadamard matrices, that can be used to construct Cretan matrices [1, 2] with orders 4t + 1, t is an integer. <...> Remarks on Extremal and Maximum Determinant Matrices with Moduand many others with the same form described above. <...> Научные базы данных, включая SCOPUS и Web of Science, обрабатывают данные автоматически. <...> Purpose: This note discusses two level quasi-orthogonal matrices which were first highlighted by J. J. Sylvester; Hadamard matrices, symmetric conference matrices, and weighing matrices are the best known of these matrices with entries from the unit disk. <...> The goal of this note is to develop a theory of such matrices based on preliminary research results. <...> Results: We present a new method aimed to give regular Hadamard matrix of order 196 and similar matrices. <...> Practical relevance: Web addresses are given for other illustrations and other matrices with similar properties. <...> Algorithms to construct regular matrices have been implemented in developing software of the research program-complex. doi:10.15217/issn1684-8853.2015.1.2 <...>
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