Geodesic
On some invariants under the action of an extension of $GA(n,2)$ on the set of Boolean functions
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 66-85

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

Let $G$ be the extension of a general affine group by the group of affine functions. We study the action of $G$ on the set of Boolean functions. The action consists in nondegenerate affine transformations of variables and addition of affine Boolean functions. We introduce and examine some parameters of Boolean functions which are invariant with respect to the action of $G$. These are the amplitude (which is closely related to the nonlinearity), the dimension of a function, and some others. The invariants, together with some additionally proposed notions, could be used to obtain new bounds on cryptographic parameters of Boolean functions, including the maximum nonlinearity of functions in an odd number of variables.
Keywords: Boolean function, discrete Fourier (Walsh–Hadamard) transform, maximum nonlinearity, amplitude, dimension of a Boolean function, extension of general affine group. 
@article{DM_2021_33_2_a5,
     author = {O. A. Logachev and S. N. Fedorov and V. V. Yashchenko},
     title = {On some invariants under the action of an extension of $GA(n,2)$ on the set of {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {66--85},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a5/}
}
TY  - JOUR
AU  - O. A. Logachev
AU  - S. N. Fedorov
AU  - V. V. Yashchenko
TI  - On some invariants under the action of an extension of $GA(n,2)$ on the set of Boolean functions
JO  - Diskretnaya Matematika
PY  - 2021
SP  - 66
EP  - 85
VL  - 33
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2021_33_2_a5/
LA  - ru
ID  - DM_2021_33_2_a5
ER  - 
%0 Journal Article
%A O. A. Logachev
%A S. N. Fedorov
%A V. V. Yashchenko
%T On some invariants under the action of an extension of $GA(n,2)$ on the set of Boolean functions
%J Diskretnaya Matematika
%D 2021
%P 66-85
%V 33
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2021_33_2_a5/
%G ru
%F DM_2021_33_2_a5
O. A. Logachev; S. N. Fedorov; V. V. Yashchenko. On some invariants under the action of an extension of $GA(n,2)$ on the set of Boolean functions. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 66-85. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a5/