Langevin, Philippe; Leander, Gregor; McGuire, Gary; Zălinescu, Eugen Analysis of Kasami-Welch functions in odd dimension using Stickelberger’s theorem. (English) Zbl 1245.11120 J. Comb. Number Theory 2, No. 1, 55-72 (2010). 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 \(\text{tr}_L(x^{2^k+1})\). Cited in 3 Documents MSC: 11T24 Other character sums and Gauss sums 06E30 Boolean functions 94C05 Analytic circuit theory Keywords:Kasami-Welch; Fourier transform; Walsh-Hadamard transform; finite field; Stickelberger; Gross-Koblitz PDFBibTeX XMLCite \textit{P. Langevin} et al., J. Comb. Number Theory 2, No. 1, 55--72 (2010; Zbl 1245.11120)