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. <...> 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. <...> 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. <...> Similar kinds of regular Hadamard matrix of order 36 were done by Jennifer Seberry (1969) [3] that inspired to find matrices of orders 4k2, k integer, 36, 100, 196, and many others. <...> The conditions for the existence request SBIBD is given in [4]. <...> Remarks on Extremal and Maximum Determinant Matrices with Moduand many others with the same form described above. <...> We apply this result to the family of regular matrices <...>