Construction of Some Block Structured (Complex) Hadamard Matrices

S. N. Topno¹ , M. K. Singh²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.124-130, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.124130

Online published on Apr 30, 2019

Copyright © S. N. Topno, M. K. Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This article investigates some methods to construct Hadamard matrices, made up of other Hadamard blocks of lower orders. Some methods are presented to construct families of real and complex block structuted Hadamard matrices using real and complex orthogonal designs together with some suitable matrices. Other new arrays are also introduced to construct block structured (complex) Hadamard matrices, along with a few methods for their constructions. Block structured (complex) Hadamard matrices have further resulted in (block structured) weighing matrices. Also infinite families of orthogonal design of order 4t and type (2t, 2t) are also constructed which depend upon the existence of Williamson matrices and Turyn-type Williamson matrices.

Key-Words / Index Term :
Hadamard matrix, weighing matrix, orthogonal design, plug-in arrays, Kronecker product

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