Geodesic
Permutation binomial functions over finite fields
Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 59-80

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

We consider binomial functions over a finite field of order $2^n$. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that $2^n-1$ is prime. Permutation binomial functions are constructed in the case when $4n$ is composite and found for $n\le8$. Tab. 2, bibliogr. 30.
Keywords: vectorial Boolean function, APN function.
Mots-clés : binomial function, permutation 
@article{DA_2018_25_4_a4,
     author = {A. V. Miloserdov},
     title = {Permutation binomial functions over finite fields},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {59--80},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2018_25_4_a4/}
}
TY  - JOUR
AU  - A. V. Miloserdov
TI  - Permutation binomial functions over finite fields
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2018
SP  - 59
EP  - 80
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2018_25_4_a4/
LA  - ru
ID  - DA_2018_25_4_a4
ER  - 
%0 Journal Article
%A A. V. Miloserdov
%T Permutation binomial functions over finite fields
%J Diskretnyj analiz i issledovanie operacij
%D 2018
%P 59-80
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2018_25_4_a4/
%G ru
%F DA_2018_25_4_a4
A. V. Miloserdov. Permutation binomial functions over finite fields. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 59-80. http://geodesic.mathdoc.fr/item/DA_2018_25_4_a4/