Hadamard matrices of order 4(2p + 1)

AbstractIt is shown in this paper that if p is a prime and q = 2p − 1 is a prime power, then there exists an Hadamard matrix of order 4(2p + 1)

Some classes of Hadamard matrices with constant diagonal

The concepts of circulant and back circulant matrices are generalized to obtain incidence matrices of subsets of finite additive abelian groups. These results are then used to show the existence of skew-Hadamard matrices of order 8(4f+l) when f is odd and 8f + 1 is a prime power. This shows the existence of skew-Hadamard matrices of orders 296, 592, 1184, 1640, 2280, 2368 which were previously unknown

Some results on weighing matrices

It is shown that if q is a prime power then there exists a circulant weighing matrix of order q2 + q + 1 with q2 non-zero elements per row and column. This result allows the bound N to be lowered in the theorem of Geramita and Wallis that given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k) of order 2n exist for every n \u3e N