Pairs of primitive elements in fields of even order

Cohen, S. D. (2014) Pairs of primitive elements in fields of even order. Finite Fields and their Applications, 28, pp. 22-42. (doi: 10.1016/j.ffa.2014.01.012)

Abstract

Let Fq be a finite field of even order. Two existence theorems, towards which partial results have been obtained by Wang, Cao and Feng, are now established. These state that (i) for any q 8, there exists a primitive element α ∈ Fq such that α + 1/α is also primitive, and (ii) for any integer n 3, in the extension of degree n over Fq there exists a primitive element α with α+ 1/α also primitive such that α is a normal element over Fq. Corresponding results for finite fields of odd order remain to be investigated.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Cohen, Professor Stephen
• Authors: Cohen, S. D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Finite Fields and their Applications
• Publisher: Elsevier
• ISSN: 1071-5797
• ISSN (Online): 1090-2465