Rational image of r-primitive k-normal elements with prescribed traces

Abstract

Let denote the degree-m extension of the finite field , where q is a prime power and m is a positive integer. Suppose and are such that divide . Let be a rational function subject to minor conditions. In this article, for , we establish a sufficient condition on the pair (q, m) that guarantees the existence of an -primitive -normal element such that trace of over is a, trace of over is b and is an -primitive -normal element in .