Regular Hadamard Matrix of Order 196 and Similar Matrices

Полный текст:


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 x q = 1 + p x (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.

Об авторах

Николай Алексеевич Балонин
Санкт-Петербургский государственный университет аэрокосмического приборостроения

M. Sergeev
Saint-Petersburg State University of Aerospace Instrumentation

Список литературы

1. Balonin N. A., Sergeev M. B. Local Maximum Determinant Matrices. Informatsionno-upravliaiushchie sistemy, 2014, no. 1(68), pp. 2-15

2. Balonin N. A., Jennifer Seberry. Remarks on Extremal and Maximum Determinant Matrices with Moduli sistemy, 2014, no. 5(72), pp. 2-4.

3. Jennifer Wallis (Seberry). Two New Block Designs. Journal of Combinatorial Theory, 1969, vol. 7, no. 4, pp. 369-368.

4. Xia T., Xia M., Seberry J. Regular Hadamard Matrices, Maximum Excess and SBIBD. AJC, 2003, vol. 27, pp. 263-275.

Дополнительные файлы

Для цитирования: Балонин Н.А., . . Информационно-управляющие системы. 2015;(1):2-3.

For citation: Balonin N.A., Sergeev M.B. Regular Hadamard Matrix of Order 196 and Similar Matrices. Information and Control Systems. 2015;(1):2-3. (In Russ.) (In Russ.)

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ISSN 1684-8853 (Print)
ISSN 2541-8610 (Online)