On the construction of Hadamard matrices by using the known Hadamard matrices

Abstract

In this paper, by the use of Latin squares, we describe a procedure to construct Hadamard matrices using the existing Hadamard matrices of order $m$ as input matrices. We propose a construction of Hadamard matrices of orders $m(m-1)$, $m(\frac{m}{2}-1)$ and $m(\frac{m}{k}-1)$, where $k$ is a multiple of four that divides $m$ into an even number. This work is a continuation of our previous one in [5](A. Farouk, Q.W. Wang, An infinite family of Hadamard matrices constructed from Paley type matrice, To appear in FILOMAT).