Bulletin of Pure and Applied Sciences Section - E - Mathematics & Statistics
  • Year: 2020
  • Volume: 39e
  • Issue: 1

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

1Department of Applied Mathematics, Adama Science and Technology University, Adama, P.O. Box. 1888, Ethiopia

†Corresponding author M.M. Nair, E-mail: madhukkdnair@yahoo.co.in

Online published on 14 August, 2020.

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.

Keywords

Hadamard matrix, Block matrix, Hadamard conjecture, 05B20, 15B34