Geodesic
Features of maximal period polynomial generators over the Galois ring
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 52-61

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

For a polynomial mapping over the Galois ring $R=\mathrm{GR}(q^n,p^n)$ with the cardinality $q^n$ and characteristic $p^n$, the maximal length of a cycle equals $q(q-1)p^{n-2}$. In this paper, we present an algorithm for constructing the system of representatives of all maximal length cycles and an algorithm for constructing an element in a cycle of maximal length for a polynomial substitution $f\in R[x]$. The complexity of the first algorithm equals $d(q-1)q^{n-1}$ multiplication operations and $d(q-1)q^{n-1}$ addition operations in $R$, the complexity of the second algorithm equals $dq$ multiplication operations and $dq$ addition operations in $R$ where $d=\deg(f)$.
Keywords: nonlinear recurrent sequences, Galois ring. 
@article{PDM_2015_1_a4,
     author = {D. M. Ermilov},
     title = {Features of maximal period polynomial generators over the {Galois} ring},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {52--61},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_1_a4/}
}
TY  - JOUR
AU  - D. M. Ermilov
TI  - Features of maximal period polynomial generators over the Galois ring
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 52
EP  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_1_a4/
LA  - ru
ID  - PDM_2015_1_a4
ER  - 
%0 Journal Article
%A D. M. Ermilov
%T Features of maximal period polynomial generators over the Galois ring
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 52-61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_1_a4/
%G ru
%F PDM_2015_1_a4
D. M. Ermilov. Features of maximal period polynomial generators over the Galois ring. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 52-61. http://geodesic.mathdoc.fr/item/PDM_2015_1_a4/