Analysis of Kasami-Welch Functions in Odd Dimension using Stickelberger's Theorem

Abstract : In this article we apply some number theoretical techniques to derive results on Boolean functions. We apply Stickelberger’s theorem on 2-adic valuations of Gauss sums to the Kasami-Welch functions trL(x4k−2k+1) on F2n , where n is odd and (k, n)= 1. We obtain information on the Fourier spectrum, including a characterization of the support of the Fourier transform. One interesting feature is that the behaviour is different for different values of k. We also apply the Gross-Koblitz formula to the Gold functions trL(x2k+1).
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https://hal.archives-ouvertes.fr/hal-01279290
Contributor : Philippe Langevin <>
Submitted on : Thursday, February 25, 2016 - 7:01:07 PM
Last modification on : Thursday, June 21, 2018 - 1:56:02 PM

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Philippe Langevin, Gregor Leander, Gary Mcguire, Eugen Zalinescu. Analysis of Kasami-Welch Functions in Odd Dimension using Stickelberger's Theorem. Journal of Combinatorics and Number Theory, 2011, 2 (1), pp.55 -- 72. ⟨hal-01279290⟩

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