Primitive element pairs with a prescribed trace in the quartic extension of a finite field

被引:6
作者
Cohen, Stephen D. [1 ]
Gupta, Anju [2 ]
机构
[1] Univ Glasgow, 6 Bracken Rd, Aberdeen AB12 4TA, Scotland
[2] Govt Coll Women, Behal Bhiwani 127028, Haryana, India
关键词
Finite field; character; primitive element;
D O I
10.1142/S0219498821501681
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we give a largely self-contained proof that the quartic extension F-q4 of the finite field F-q contains a primitive element alpha such that the element alpha + alpha(-1) is also a primitive element of F-q4, and TrF (q4|Fq)(alpha) = a for any prescribed a is an element of F-q. The corresponding result has already been established for finite field extensions of degrees exceeding 4 in [Primitive element pairs with one prescribed trace over a finite field, Finite Fields Appl. 54 (2018) 1-14.].
引用
收藏
页数:14
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