Primitive elements on lines in extensions of finite fields

Cohen, S.D. (2010) Primitive elements on lines in extensions of finite fields. In: McGuire, G., Mullen, G.L., Panario, D. and Shparlinski, I.E. (eds.) Finite Fields: Theory and Applications. Series: Contemporary Mathematics (518). American Mathematical Society: Providence, RI, pp. 113-127. ISBN 978-0-8218-4786-2

Abstract

Given an integer n > 1, for which prime powers q does every translate {0 + a : a is an element of F-q} (with F-q(theta) = F(q)n) contain a primitive element of F(q)n? Further, for which prime powers does every line {alpha(0 + a) : a is an element of F-q} (with F-q(theta) = F(q)n and alpha (not equal 0) is an element of F(q)n) contain a primitive element? This paper incorporates a review of explicit results for n <= 4.

• Item Type: Book Sections
• Additional Information: 9th International Conference on Finite Fields and Applications Dubin, IRELAND, JUL 13-17, 2009
• Status: Published
• Glasgow Author(s) Enlighten ID: Cohen, Professor Stephen
• Authors: Cohen, S.D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: American Mathematical Society
• ISBN: 978-0-8218-4786-2