On strong orthogonal systems and weak permutation polynomials over finite commutative rings

被引：3
|
作者：
Wei, Qijiao
Zhang, Qifan [1 ]
机构：
[1] Sichuan Univ, Coll Math, Chengdu 610064, Peoples R China
[2] Chengdu Univ Informat Technol, Dept Computat Sci, Chengdu, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2007年 / 13卷 / 01期
基金：
中国国家自然科学基金;
关键词：
permutation polynomial; orthogonal system; finite field; finite local ring;
D O I：
10.1016/j.ffa.2005.08.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study two kinds of orthogonal systems of polynomials over finite commutative rings and get two fundamental results. Firstly, we obtain a necessary and sufficient condition for a system of polynomials (over a fixed finite commutative ring R) to form a strong orthogonal system. Secondly, for a pair (R, n) of a finite local ring R and an integer n > 1, we get an easy criterion to check whether every weak permutation polynomial in n variables over R is strong. (c) 2005 Elsevier Inc. All rights reserved.
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页码：113 / 120
页数：8
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