Geodesic
On derivatives of Boolean bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 57-58

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Bent function can be defined as a Boolean function $f(x)$ in $n$ variables ($n$ is even) such that for any nonzero vector $y$ its derivative $D_yf(x)=f(x)\oplus f(x\oplus y)$ is balanced, that is, it takes values $0$ and $1$ equally often. Whether every balanced function is a derivative of some bent function or not is an open problem. In this paper, special case of this problem is studied. It is proven that every non-constant affine function in $n$ variables, $n\geqslant4$, $n$ is even, is a derivative of $(2^{n-1}-1)|\mathcal{B}_{n-2}|^2$ bent functions, where $|\mathcal{B}_{n-2}|$ is the number of bent functions in $n-2$ variables. New iterative lower bounds for the number of bent functions are presented.
Keywords: Boolean functions, bent functions, derivatives of bent function, lower bounds for the number of bent functions. 
A. S. Shaporenko. On derivatives of Boolean bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 57-58. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a11/
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