Hadamard matrices, strongly regular graphs, and Galois fields

Abstract

In this paper the author uses the concept of circulant matrices and the superposition principle to find, from the adjacency matrices of three regular graphs of order 8 and degree 2, tire adjacency matrix, M, of a strongly regular graph G(8,6,4,6). M is then decomposed, by means of addition subtraction, and the Kronecker product of matrices, to get the Hadamard matrix OH(2,4). Finally, the paper shows how the row vectors of this matrix can be found by using the elements of the finite field GF(2), and the concept of the T-character.