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- Title
Primitive Finite Field Elements with Prescribed Trace.
- Authors
Cohen, Stephen D.; Prešern, Mateja
- 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.
- Subjects
INTEGRAL theorems; FINITE fields; LOGICAL prediction; INTEGRALS; ABSTRACT algebra
- Publication
Southeast Asian Bulletin of Mathematics, 2005, Vol 29, Issue 2, p283
- ISSN
0129-2021
- Publication type
Article