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.

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• 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
• ISSN: 0129-2021