Autocorrelation of Legendre–Sidelnikov Sequences

We combine the concepts of the p-periodic Legendre sequence, the (q-1)-periodic Sidelnikov sequence and the two-prime generator to introduce a new p(q-1)-periodic sequence called Legendre-Sidelnikov sequence. We show that this new sequence is balanced if p=q. For an arbitrary odd prime p and an arbitrary power q of an odd prime with gcd (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.