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

In this paper, we give a largely self-contained proof that the quartic extension q 4 of the finite field q contains a primitive element α such that the element α + α − 1 is also a primitive element of q 4 , and Tr q 4 | q (α) = a for any prescribed a ∈ 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.]. [ABSTRACT FROM AUTHOR]