
doi: 10.1007/bf01212983
A \((1,-1)\)-matrix \(A\) of order \(m\) is an Hadamard matrix if \(AA^ T= mI_ m\) (\(A^ T\) is the transpose of \(A\), and \(I_ m\) is the identity matrix of order \(m\)). If such \(A\) exists and \(m> 2\) then \(4| m\) and we write \(m= 4n\). There exists an Hadamard matrix of order 2. Since the tensor product of Hadamard matrices is again an Hadamard matrix, one is mainly interested in constructing Hadamard matrices of order \(m= 4n\) for \(n\) odd. According to the literature, Hadamard matrices of order \(4n\) are known for all \(n\leq 500\), except for the following 17 values of \(n\): 107, 167, 179, 191, 223, 239, 251, 283, 311, 347, 359, 419, 443, 478, 479, 487, 491. Note that all these numbers are primes congruent to \(3\pmod 4\), except for \(478= 2\cdot 239\). In this paper, the author constructs two Hadamard matrices of order \(4\cdot 239= 956\) which are of special type, known as Hadamard matrices of Goethals-Seidel type. Consequently the numbers 239 and 478 should be removed from the above list.
Hadamard matrix, Goethals-Seidel type, Other designs, configurations, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Hadamard matrix, Goethals-Seidel type, Other designs, configurations, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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