Primitive finite field elements with prescribed trace

Cohen, S. and Presern, M. (2005) Primitive finite field elements with prescribed trace. Southeast Asian Bulletin of Mathematics, 29(2), pp. 283-300.

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Cohen, Professor Stephen and Presern, Dr Mateja
Authors: Cohen, S., and Presern, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Southeast Asian Bulletin of Mathematics

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