New Hadamard matrices and conference matrices obtained via Mathon's construction

We give a formulation, via (1, 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·92r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.92r+1+ 2, 10.92t+1 + 2, 8·49·92, t ≥ 0; q2(q + 3) + 2 where q ≡ 3 (mod 4) is a prime power and 1/2(q + 5) is the order of a skew-Hadamard matrix); (q + 1)q2.9t, t ≥ o (where q ≡ 7 (mod 8)is a prime power and 1/2(q + 1) is the order of an Hadamard matrix). We also give new constructions for Hadamard matrices of order 4·9' ≥ 0 and (q + l)q2 (where q ≡ 3 (mod 4) is a prime power). Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Whiteman, AL, New Hadamard matrices and conference matrices obtained via Mathon's construction, Graphs and Combinatorics, 4, 1988, 355-377. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1032