Geodesic
Nonlinearity of functions over finite fields
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 110-131

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

The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity.
Keywords: nonlinearity, finite field, Fourier coefficients, autocorrelation, bent function, translator. 
@article{DM_2021_33_4_a9,
     author = {V. G. Ryabov},
     title = {Nonlinearity of functions over finite fields},
     journal = {Diskretnaya Matematika},
     pages = {110--131},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_4_a9/}
}
TY  - JOUR
AU  - V. G. Ryabov
TI  - Nonlinearity of functions over finite fields
JO  - Diskretnaya Matematika
PY  - 2021
SP  - 110
EP  - 131
VL  - 33
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2021_33_4_a9/
LA  - ru
ID  - DM_2021_33_4_a9
ER  - 
%0 Journal Article
%A V. G. Ryabov
%T Nonlinearity of functions over finite fields
%J Diskretnaya Matematika
%D 2021
%P 110-131
%V 33
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2021_33_4_a9/
%G ru
%F DM_2021_33_4_a9
V. G. Ryabov. Nonlinearity of functions over finite fields. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 110-131. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a9/