TY - JOUR AU - Николай Алексеевич Балонин AU - Михаил B. Сергеев PY - 2015/02/20 Y2 - 2024/03/28 TI - Regular Hadamard Matrix of Order 196 and Similar Matrices JF - Информационно-управляющие системы JA - ИУС VL - 0 IS - 1 SE - Теоретическая и прикладная математика DO - 10.15217/issn1684-8853.2015.1.2 UR - https://i-us.ru/index.php/ius/article/view/4200 AB - 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 4k ER -