Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895571 | Finite Fields and Their Applications | 2018 | 14 Pages |
Abstract
In this article, we establish a sufficient condition for the existence of a primitive element αâFqn such that the element α+αâ1 is also a primitive element of Fqn, and TrFqn|Fq(α)=a for any prescribed aâFq, where q=pk for some prime p and positive integer k. We prove that every finite field Fqn(nâ¥5), contains such primitive elements except for finitely many values of q and n. Indeed, by computation, we conclude that there are no actual exceptional pairs (q,n) for nâ¥5.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anju Gupta, R.K. Sharma, Stephen D. Cohen,