Generalization of Scarpis’ theorem on Hadamard matrices
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Abstract
A -matrix H of order m is a Hadamard matrix if , where T is the transposition operator and is the identity matrix of order m. J. Hadamard published his well known paper on Hadamard matrices in 1893. Five years later, Scarpis showed how one can use a Hadamard matrix of order , a prime, to construct a bigger Hadamard matrix of order pn. In this note we show that Scarpis’ construction can be extended to the more general case where p is replaced by a prime power q but still .
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