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Analysis of Kasami-Welch functions in odd dimension using Stickelberger’s theorem. (English) Zbl 1245.11120

Summary: 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 \(\text{tr}_L(x^{4^k-2^k+1})\) on \(\mathbb F_{2^n}\), 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 \(\text{tr}_L(x^{2^k+1})\).

MSC:

11T24 Other character sums and Gauss sums
06E30 Boolean functions
94C05 Analytic circuit theory
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