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Autocorrelation of Legendre–Sidelnikov Sequences

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2 Author(s)
Ming Su ; Dept. of Comput. Sci., Nankai Univ., Tianjin, China ; Winterhof, A.

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.

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Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 4 )