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.
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页码：931 / 947
页数：17
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