EXAMPLE OF LEGENDRE SEQUENCE


       Transformation of Legendre sequences
 

 If $v\equiv 3 \mod 4$ then we can tranform the Legendre sequence $s$ in a binary sequence $r$ by
\begin{displaymath}r(x) = \delta_0(x) + s(x)\end{displaymath}
the out-phase correlations are unchanged since
\begin{displaymath}r\times r(\tau) = \delta_0(\tau) + s(\tau) + s(-\tau) +s\times s(\tau)\end{displaymath}