Full paper in PDF:
$% I. E. Shparlinski, On the number of zero trace elements in polynomial bases for F2n, Rev. Mat. Complut. 18 (2005), no. 1, 177–180.%$

On the Number of Zero Trace Elements in Polynomial Bases for F2n

Igor E. SHPARLINSKI
Department of Computing
Macquarie University
Sydney, NSW 2109 Australia

Received: June 16, 2004
Accepted: July 8, 2004
ABSTRACT

Let Fq  denotes the finite field of q  elements. O. Ahmadi and A. Menezes have recently considered the question about the possible number of elements with zero trace in polynomial bases of F2n  over F2  . Here we show that the Weil bound implies that there is such a basis with n+ O(log n)  zero-trace elements.

Key words: bases of finite fields, Weil bound.
2000 Mathematics Subject Classification:
11T30, 11T71, 9460.