Abstract
Let F= GF( q) and let E = GF( q k ) be the field extension of degree k of F. We show that the following statement holds for all but finitely many exceptional pairs ( q, k): Given any element aϵF ∗ there exists a primitive element ω of E with trace T E F (ω) = a . Equivalently, the coefficient of x k − 1 in a primitive polynomial of degree k over GF( q) may be arbitrarily selected from GF(q) ∗ .
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