A modification of Fitzgerald's characterization of primitive polynomials over a finite field

被引：1

作者：

Laohakosol, Vichian ^{[1
]}

Pintoptang, Umarin ^{[2
]}

机构：

[1] Kasetsart Univ, Dept Math, Bangkok 10900, Thailand

[2] Naresuan Univ, Dept Math, Phitsanulok 65000, Thailand

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2008年 / 14卷 / 01期

关键词：

finite field; primitive polynomial; linear recurring sequence;

D O I：

10.1016/j.ffa.2007.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A characterization of primitive polynomials, among irreducible polynomials, over a finite field is established. Such characterization is determined by the number of nonzero terms in certain quotient of polynomials. The proof, which is a modification of the one discovered by Fitzgerald in 2003 yet revealing more general structure, is based principally on counting the number of occurrences of elements in a linear recurring sequence over a finite field. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：85 / 91

页数：7

共 6 条

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