Geodesic
An additive approach to nonlinearity degree of discrete functions on a primary cyclic group
Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 26-38

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

An additive approach to the definition of nonlinearity degree for a discrete function on a cyclic group is proposed. For elementary abelian groups, this notion is equivalent to the ordinary “multiplicative” one. For polynomial functions on the ring of integers $\mod p^n$, this notion is equivalent to the minimal degree of a polynomial. It is proved that the nonlinearity degree on a cyclic group is a finite number if and only if the order of the group is a power of a prime. An upper bound for the nonlinearity degree of functions on a cyclic group of order $p^n$ is given.
Keywords: discrete functions, nonlinearity degree. 
A. V. Cheremushkin. An additive approach to nonlinearity degree of discrete functions on a primary cyclic group. Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 26-38. http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/
@article{PDM_2013_2_a3,
     author = {A. V. Cheremushkin},
     title = {An additive approach to nonlinearity degree of discrete functions on a~primary cyclic group},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {26--38},
     year = {2013},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/}
}
TY  - JOUR
AU  - A. V. Cheremushkin
TI  - An additive approach to nonlinearity degree of discrete functions on a primary cyclic group
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2013
SP  - 26
EP  - 38
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/
LA  - ru
ID  - PDM_2013_2_a3
ER  - 
%0 Journal Article
%A A. V. Cheremushkin
%T An additive approach to nonlinearity degree of discrete functions on a primary cyclic group
%J Prikladnaâ diskretnaâ matematika
%D 2013
%P 26-38
%N 2
%U http://geodesic.mathdoc.fr/item/PDM_2013_2_a3/
%G ru
%F PDM_2013_2_a3

[1] Cheremushkin A. V., “Additivnyi podkhod k opredeleniyu stepeni nelineinosti diskretnoi funktsii”, Prikladnaya diskretnaya matematika, 2010, no. 2(8), 22–33

[2] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Uchebnik v 2-kh t., v. II, Gelios ARV, M., 2003

[3] Keller G., Olson F., “Counting polynomial functions (mod $p^n$)”, Duke Math. J., 35 (1968), 835–838 | DOI | MR | Zbl

[4] Chen Z., “On polynomial functions from $\mathbb Z_{n_1}\times\mathbb Z_{n_2}\times\dots\mathbb Z_{n_r}$ to $\mathbb Z_m$”, Discrete Math., 162 (1996), 67–76 | DOI | MR | Zbl

[5] Davio M., Deschamps J. P., Thayse A., Discrete and switching functions, Academiai Kiado, Budapest, 1974