EXISTENCE RESULTS FOR PRIMITIVE ELEMENTS IN CUBIC AND QUARTIC EXTENSIONS OF A FINITE FIELD

被引：5

作者：

Bailey, Geoff ^{[1
]}

Cohen, Stephen D. ^{[2
]}

Sutherland, Nicole ^{[1
]}

Trudgian, Tim ^{[3
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Computat Algebra Grp, Camperdown, NSW 2006, Australia

[2] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QQ, Lanark, Scotland

[3] Australian Def Force Acad, UNSW Canberra, Sch Phys Environm & Math Sci, Campbell, ACT 2610, Australia

来源：

MATHEMATICS OF COMPUTATION | 2019年 / 88卷 / 316期

基金：

澳大利亚研究理事会;

关键词：

Primitive elements; finite fields; cubic generators;

D O I：

10.1090/mcom/3357

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

With F-q the finite field of q elements, we investigate the following question. If gamma generates F-qn over F-q and if beta is a nonzero element of F-qn, is there always an a is an element of F-q such that beta(gamma + a) is a primitive element? We resolve this case when n = 3, thereby proving a conjecture by Cohen. We also substantially improve on what is known when n = 4.

引用

页码：931 / 947

页数：17

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