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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

\begin{displaymath}
m = 2^e (q^n + 1),
\end{displaymath}

$q$ is an Odd Prime, and

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

See also Hadamard Matrix, Paley Construction




© 1996-9 Eric W. Weisstein
1999-05-26