Dickson polynomials over finite fields

被引：27

作者：

Wang, Qiang ^{[1
]}

Yucas, Joseph L. ^{[2
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[2] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2012年 / 18卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Finite fields; Dickson polynomials; Permutation polynomials; Factorization; DECOMPOSITION; PERMUTATIONS;

D O I：

10.1016/j.ffa.2012.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce the notion of Dickson polynomials of the (k + 1)-th kind over finite fields F-pm and study basic properties of this family of polynomials. In particular, we study the factorization and the permutation behavior of Dickson polynomials of the third kind. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：814 / 831

页数：18

共 9 条

[1] Factoring Dickson polynomials over finite fields
Bhargava, M
Zieve, ME
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 1999, 5 (02) : 103 - 111
[2] Chou W.-S., 1997, FINITE FIELDS APPL, V3, P84
[3] Cipu M., 2004, SERDICA MATH J, V30, P177
[4] Cipu M, 2008, CONTEMP MATH, V461, P79
[5] DICKSON POLYNOMIALS OF THE 2ND KIND THAT ARE PERMUTATIONS
COHEN, SD
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1994, 46 (02): : 225 - 238
[6] Decomposition of a recursive family of polynomials
Dujella, Andrej
Gusic, Ivica
[J]. MONATSHEFTE FUR MATHEMATIK, 2007, 152 (02): : 97 - 104
[7] Reversed Dickson polynomials over finite fields
Hou, Xiang-dong
Mullen, Gary L.
Sellers, James A.
Yucas, Joseph L.
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (06) : 748 - 773
[8] Lidl R., 1993, Dickson Polynomials
[9] Complete decomposition of Dickson-type polynomials and related Diophantine equations
Stoll, Thomas
[J]. JOURNAL OF NUMBER THEORY, 2008, 128 (05) : 1157 - 1181

← 1 →