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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DA_2014_21_2_a3,
     author = {N. A. Kolomeec},
     title = {A threshold property of quadratic {Boolean} functions},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {52--58},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2014_21_2_a3/}
}
TY  - JOUR
AU  - N. A. Kolomeec
TI  - A threshold property of quadratic Boolean functions
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2014
SP  - 52
EP  - 58
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2014_21_2_a3/
LA  - ru
ID  - DA_2014_21_2_a3
ER  - 
%0 Journal Article
%A N. A. Kolomeec
%T A threshold property of quadratic Boolean functions
%J Diskretnyj analiz i issledovanie operacij
%D 2014
%P 52-58
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2014_21_2_a3/
%G ru
%F DA_2014_21_2_a3
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/