Jacobi Sums and Correlations of Sidelnikov Sequences

02/15/2019

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by   Ayse Alaca, et al.

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We consider the problem of determining the cross-correlation values of the sequences in the families comprised of constant multiples of M-ary Sidelnikov sequences over F_q, where q is a power of an odd prime p. We show that the cross-correlation values of pairs of sequences from such a family can be expressed in terms of certain Jacobi sums. This insight facilitates the computation of the cross-correlation values of these sequence pairs so long as ϕ(M)^ϕ(M)≤ q. We are also able to use our Jacobi sum expression to deduce explicit formulae for the cross-correlation distribution of a family of this type in the special case that there exists an integer x such that p^x ≡ -1 M.