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

M M  Nair

doi:10.48165/

Authors

M M Nair Department of Applied Mathematics, Adama Science and Technology University, Adama, P.O. Box. 1888, Ethiopia.

DOI:

https://doi.org/10.48165/

Keywords:

Hadamard matrix, Block matrix, Hadamard conjecture

Abstract

In this paper we consider a symmetric matrix A2 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 A2. From this special square matrix A2 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.

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