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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2020, Volume & Issue : BPAS-Maths & Stat 39E(1), JAN-JUN 2020
Page No. : 77-83, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2020.00006.5 (Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief). Received November 24, 2018 / Revised July 17, 2019 / Accepted August 09, 2019. Online First Published on June 30, 2020)

On the existence of a special type of symmetric matrix and the construction of Hadamard matrices

M.M. Nair1
Author’s Affiliation : 1. Department of Applied Mathematics, Adama Science and Technology University, Adama, P.O. Box. 1888, Ethiopia. 1. E-mail: [email protected]

Corresponding Author : M.M. Nair,
E-Mail:-[email protected]


Abstract

In this paper  we consider a symmetric matrix $A^{2} $ which is the square of an unknown matrix $A$ with only the two numbers $+1$ and $-1$ as its entries and we establish the existence of a special type of square matrix $A^{2} $. From this special square matrix $A^{2} $ all the possible matrices $A$ can be obtained and used for the construction of Hadamard matrices. These Hadamard matrices are much useful in coding theory, communication theory, signal processing and cryptography.

Keywords

Hadamard matrix, Block matrix, Hadamard conjecture. 2020 Mathematics Subject Classification: 05B20, 15B34.
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