Abstract

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{dot operator}92 t+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{dot operator}92 t+1 + 2, 10{dot operator}92 t+1 + 2, 8{dot operator}49{dot operator}9t, 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 skewHadamard matrix); (q + 1)q2{dot operator}9t, t ≥ 0 (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{dot operator}9t ≥ 0 and (q + 1)q2 (where q ≡ 3 (mod 4) is a prime power). © 1988 SpringerVerlag.