Paley's Theorem

Proved in 1933. If q is an odd prime or q=0 and n is any positive integer, then there is a Hadamard matrix of order


where e is any positive integer such that m=0 (mod 4). If m is of this form, the matrix can be constructed with a Paley construction. If m is divisible by 4 but not of the form (1), the Paley class is undefined. However, Hadamard matrices have been shown to exist for all m=0 (mod 4) for m<668.

See also

Hadamard Graph, Hadamard Matrix, Paley Class, Paley Construction, Paley Graph

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Cite this as:

Weisstein, Eric W. "Paley's Theorem." From MathWorld--A Wolfram Web Resource.

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