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⋅92t+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⋅92t+1 + 2, 10⋅92t+1 + 2, 8⋅49⋅9t,t ≥ 0;q2(q + 3) + 2 whereq ≡ 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 ≥ 0 (whereq ≡ 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⋅9t ≥ 0 and (q + 1)q2 (whereq ≡ 3 (mod 4) is a prime power).