The skew - weighing matrix conjecture

We review the history of the skew-weighing matrix conjecture and show that there exist skew-symmetric weighing matrices W (21.2t, k) for all k=0,l,.....,21.2t - I, t ≥ 4 a positive integer. Hence there exist orthogonal designs of type l(l,k) for all k=O,l,..., 21.2t - 1, t ≥ 4 a positive integer, in order 21.2t.