Pair of primitive elements with prescribed traces over finite fields
R. K. Sharma, Anju Gupta · Communications in Algebra · 2019
In this article, we establish a sufficient condition for the existence of a primitive element α∈Fqn such that for any matrix (abc0de)∈M2×3(Fqn) of rank 2, the element (aα2+bα+c)/(dα+e) is a primitive element of Fqn, and TrFqn|Fq(α)=μ, TrFqn|Fq(α−1)=ν for any prescribed μ,ν∈Fq, where q=2k for some positive integer k. We establish existence of such elements for all pairs (q,n) (n≥7) except for finitely many pairs.