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

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

See also Hadamard Matrix, Paley Construction