Let a Boolean function in n variables be affine on an affine subspace of dimension |~n/2] if and only if f is affine on any its shift. It is proved that algebraic degree of f can be more than 2 only if there is no affine subspace of dimension [n/2] that f is affine on it.
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- Title An affine property of boolean functions on subspaces and their shifts
- Headline An affine property of boolean functions on subspaces and their shifts
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 6 (Приложение)
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Keywords
булевы функции, бент-функции, квадратичные функции, Boolean functions, bent functions, quadratic functionsAuthors
References
Rothaus O. On bent functions // J. Combin. Theory. Ser.A. 1976. V.20. No.3. P. 300-305.
Токарева Н. Н. Нелинейные булевы функции: бент-функции и их обобщения. Saarbrucken: LAP LAMBERT Academic Publishing, 2011.
Коломеец Н. А., Павлов А. В. Свойства бент-функций, находящихся на минимальном расстоянии друг от друга // Прикладная дискретная математика. 2009. №4. С. 5-20.
An affine property of boolean functions on subspaces and their shifts | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 6 (Приложение).
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