Skew Hadamard matrices of Goethals-Seidel type

Goethals and Seidel have recently demonstrated the existence of skew Hadamard matrices of orders 36 and 52 by means of a new type of construction. Jennifer Wallis has obtained additional matrices of this type for all orders 4n, 3 < n < 25 and n odd. In the present paper, an infinite family of such matrices is derived. The main result states that if q is a prime power = 3(mod 8), then there exists a skew Hadamard matrix of order 4n = q + 1 that is of the Goethals-Seidel type.

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