The trace of 2-primitive elements of finite fields
Volume 192 / 2020
Acta Arithmetica 192 (2020), 397-419
MSC: Primary 11T30; Secondary 11T06.
DOI: 10.4064/aa190307-23-5
Published online: 29 November 2019
Abstract
Let be a prime power and n, r integers such that r\,|\, q^n-1. An element of \mathbb F _{q^n} of multiplicative order (q^n-1)/r is called r-primitive. For any odd prime power q, we show that there exists a 2-primitive element of \mathbb F _{q^n} with arbitrarily prescribed \mathbb F _q-trace when n\geq 3. Also we explicitly describe the values that the trace of such elements may have when n=2.
