New Hadamard matrices and conference matrices obtained via Mathon's construction (Q1120580)

A theorem by \textit{R. Mathon} [Can. J. Math. 30, 321-331 (1978; Zbl 0385.05018)] states that there are symmetric conference matrices of order \((q+2)q^ 2+1\) when \(q=4t-1\) is a prime power and \(q+3\) is the order of a conference matrix. The authors investigate Mathon's construction by a direct formulation of the matrices he uses in terms of (1,-1) matrices. These matrices are then generalized and used to find new constructions for families of Hadamard and conference matrices. Among others, this procedures gives a new conference matrix of order 3646 and a new Hadamard marix of order 7292.