Dynamics of polynomial maps over finite fields

被引：4

作者：

Oliveira, Jose Alves ^{[1
]}

Martinez, F. E. Brochero ^{[2
]}

机构：

[1] Univ Fed Lavras, UFLA, Dept Matemat, BR-37200900 Lavras, MG, Brazil

[2] Univ Fed Minas Gerais, UFMG, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2024年 / 92卷 / 05期

基金：

巴西圣保罗研究基金会;

关键词：

Functional graph; Polynomial maps; Finite fields; Finite abelian group; FUNCTIONAL GRAPHS;

D O I：

10.1007/s10623-023-01332-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let F-q be a finite field with q elements and let n be a positive integer. In this paper, we study the digraph associated to the map x -> x(n)h(x (q-1/m)) over F-q, where h(x) is an element of F-q [x]. We completely determine the associated functional graph of maps that satisfy a certain condition of regularity. In particular, we provide the functional graphs associated to monomial maps. As a consequence of our results, one have the number of connected components, length of the cycles and number of fixed points of these class of maps.

引用

页码：1113 / 1125

页数：13

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