On the Existence of Pairs of Primitive and Normal Elements Over Finite Fields

被引：5

作者：

Carvalho, Cicero ^{[1
]}

Guardieiro, Joao Paulo ^{[1
]}

Neumann, Victor G. L. ^{[1
]}

Tizziotti, Guilherme ^{[1
]}

机构：

[1] Univ Fed Uberlandia, Fac Matemat, Av JN Avila 2121,38, BR-408902 Uberlandia, MG, Brazil

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2022年 / 53卷 / 03期

关键词：

Primitive element; Normal element; Normal basis; Finite fields;

D O I：

10.1007/s00574-021-00277-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-qn be a finite field with q(n) elements, and let m(1) and m(2) be positive integers. Given polynomials f(1)(x), f(2)(x) is an element of F-qn [x] with deg(f(i)(x)) <= m(i), for i = 1, 2, and such that the rational function f(1)(x)/ f(2)(x) satisfies certain conditions which we define, we present a sufficient condition for the existence of a primitive element alpha is an element of F-qn, normal over F-q, such that f(1)(alpha)/f(2)(a) is also primitive.

引用

页码：677 / 699

页数：23

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