Jacobi Sums and Correlations of Sidelnikov Sequences

2019/02/15 by Ayşe Alaca, Alaca, Ayse, Goldwyn Millar +1
Computer Science · Mathematics · #Coding theory and cryptography #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1902.06728

Abstract

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 \mathbbF_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 \pmodM.

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