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On the Density of Normal Bases in Finite Fields

✍ Scribed by Gudmund Skovbjerg Frandsen

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
164 KB
Volume
6
Category
Article
ISSN
1071-5797

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✦ Synopsis

Let %

O L denote the "nite "eld with qL elements, for q a prime power. % O L may be regarded as an n-dimensional vector space over % O . 3% O L generates a normal basis for this vector space (% O L :% O ), if + , O, q , 2 , O L\ , are linearly independent over % O . Let N O (n) denote the number of elements in % O L that generate a normal basis for % O L :% O , and let O (n)"N O (n)/qL denote the frequency of such elements. We show that there exists a constant c'0 such that O (n) 5 c 1 (U log O n V , for all n, q52 and this is optimal up to a constant factor in that we show 0.284774 lim L inf O (n)(log O n40.61910, for all q52.

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