Geodesic
The number of maximal period polynomial mappings over the Galois fields of odd characteristics
Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 85-100

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

Let $R = GR(q^n, p^n)$ be a Galois ring of cardinality $q^n$ and characteristics $p^n$, where $q = p^m$, $m, n > 1$. Let the sequence $U = \{u_i\}$ is defined by equations $u_{i+1} = f(u_i)$, $i \in \mathbb N_0$, and $f$ be a polynomial mapping of the ring $R$. It was proved earlier that the maximal possible period of $U$ equals $q(q-1)p^{n-2}$. Here we find the number of polynomial mappings over $R$ having maximal possible periods for $p\ne2$. 
@article{MVK_2018_9_a4,
     author = {D. M. Ermilov},
     title = {The number of maximal period polynomial mappings over the {Galois} fields of odd characteristics},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {85--100},
     publisher = {mathdoc},
     volume = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2018_9_a4/}
}
TY  - JOUR
AU  - D. M. Ermilov
TI  - The number of maximal period polynomial mappings over the Galois fields of odd characteristics
JO  - Matematičeskie voprosy kriptografii
PY  - 2018
SP  - 85
EP  - 100
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2018_9_a4/
LA  - ru
ID  - MVK_2018_9_a4
ER  - 
%0 Journal Article
%A D. M. Ermilov
%T The number of maximal period polynomial mappings over the Galois fields of odd characteristics
%J Matematičeskie voprosy kriptografii
%D 2018
%P 85-100
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2018_9_a4/
%G ru
%F MVK_2018_9_a4
D. M. Ermilov. The number of maximal period polynomial mappings over the Galois fields of odd characteristics. Matematičeskie voprosy kriptografii, Tome 9 (2018), pp. 85-100. http://geodesic.mathdoc.fr/item/MVK_2018_9_a4/