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Paley Class

The Paley class of a Positive Integer $m\equiv 0\ \left({{\rm mod\ } {4}}\right)$ is defined as the set of all possible Quadruples $(k, e, q, n)$ where

m = 2^e (q^n + 1),

$q$ is an Odd Prime, and

0 & if $q = 0$\cr
1 & if $q^n-3\equiv 0\ \left({...
...({{\rm mod\ } {4}}\right)$\cr
{\rm undefined} & otherwise.\cr}

See also Hadamard Matrix, Paley Construction

© 1996-9 Eric W. Weisstein