PERMUTATION BINOMIALS OVER FINITE FIELDS

被引：37

作者：

Masuda, Ariane M. ^{[1
]}

Zieve, Michael E. ^{[2
]}

机构：

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

[2] Ctr Commun Res, Princeton, NJ 08540 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 08期

关键词：

Permutation polynomial; finite field; Weil bound; POLYNOMIALS; NUMBER;

D O I：

10.1090/S0002-9947-09-04578-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if x(m) + ax(n) permutes the prime field F(p), where m > n > 0 and a is an element of F(p)*, then gcd(m - n,p - 1) > root p - 1. Conversely, we prove that if q >= 4 and m > n > 0 are fixed and satisfy gcd(m - n, q - 1) > 2q(log log q) / log q, then there exist permutation binomials over F(q) of the form x(m) + ax(n) if and only if gcd(m, n, q - 1) = 1.

引用

页码：4169 / 4180

页数：12

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