Primitive finite field elements with prescribed trace

Stephen D. Cohen, Mateja Presern

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)283-300
Number of pages18
JournalSoutheast Asian Bulletin of Mathematics
Issue number2
Publication statusPublished - 2005


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