Construct Hadamard matrices by means of several groups and prime numbers

Leka, Hizer (2018) Construct Hadamard matrices by means of several groups and prime numbers. Journal of Natural Sciences and Mathematics of UT, 3 (5-6). pp. 208-216. ISSN 2671-3039

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Abstract

Hadamard matrix, is a square matrix, the elements of which are either 1 or -1 and its rows mutually orthogonal. They have great application in computer science and communication technology. The most important open question in Hadamard matrix theory is that of their existence. There are several methods for constructing them. It will be shown that two classic methods for the Hadamard matrix construct, that of Paley and Williamson, can be unified and Paley and Williamson's method can be constructed with a uniform method by producing a association scheme or coherent configuration from group action to a community and the production of Hadamard matrices, taking appropriate linear combinations (1,-1) of the matrix representation of coherent configuration. For example, through the orbits of the group, the matrices of group representation orbits are taken and eventually the sum of these matrices gives a Hadamard matrix. Thus, Hadamard matrices are constructed by group’s action in the community. It will also be shown that using the Legendre symbol, the prime numbers and congruences according to the module, the first row of the Hadamard matrix is formed, then the other rows of the Hadamard matrix are taken cyclically and thus obtained a Hadamard order matrix .

Item Type:	Article
Subjects:	Q Science > Q Science (General)
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	05 Jun 2019 08:34
Last Modified:	05 Jun 2019 08:34
URI:	http://eprints.unite.edu.mk/id/eprint/164

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