Autocorrelation of Legendre–Sidelnikov Sequences

We combine the concepts of thep-periodic Legendre sequence, the(q-1)-periodic Sidelnikov sequence and the two-prime generator to introduce a newp(q-1)-periodic sequence called Legendre-Sidelnikov sequence. We show that this new sequence is balanced ifp=q. For an arbitrary odd primepand an arbitrary powerqof an odd prime withgcd (p,q-1)=1 we determine the exact values of its (periodic) autocorrelation function and deduce an upper bound on its aperiodic autocorrelation function showing that it is small compared to its period.