Geodesic
A threshold property of quadratic Boolean functions
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 52-58.

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Let $f$ be a Boolean function in $n$ variables and for any affine subspace $L$ of dimension $\lceil n/2\rceil$ either $f$ is affine on all shifts of $L$ or $f$ is not affine on any shift of $L$. It is proved that the algebraic degree of $f$ can be more than 2 only if there is no affine subspace of dimension $\lceil n/2\rceil$ that $f$ is affine on. Bibliogr. 8.
Keywords: Boolean function, quadratic Boolean function, bent function. 
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N. A. Kolomeec. A threshold property of quadratic Boolean functions. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 52-58. http://geodesic.mathdoc.fr/item/DA_2014_21_2_a3/

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