Showing papers in "Southeast Asian Bulletin of Mathematics in 2005"

Primitive finite field elements with prescribed trace

Abstract: This paper contains a self-contained, minimal computational account of Cohen's 1990 theorem that there exists a primitive element of a given finite field with arbitrary prescribed trace over a subfield The only non-trivial exception is that there is no primitive element in the 64-element field with trace zero over the 4-element field The original proof was deduced from a number of results on different themes, involving more computation and direct verification Consequently, the proof is more in tune with current general approaches to the 1992 Hansen-Mullen primitivity conjecture