Since 2014
On the Density of Normal Bases in Finite Fields
BRICS Report Series
View Archive Info| Field | Value | |
| Title |
On the Density of Normal Bases in Finite Fields
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| Creator |
Frandsen, Gudmund Skovbjerg
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| Description |
Let Fqn denote the finite field with q^n elements, for q being a prime power. Fqn may be regarded as an n-dimensional vector space over Fq. alpha in Fqn generates a normal basis for this vector space (Fqn : Fq), if{alpha, alpha^q, alpha^q^2 , . . . , alpha^q^(n−1)} are linearly independent over Fq. Let N(q; n) denote the number of elements in Fqn that generate a normal basis forFqn : Fq, and let nu(q, n) = N(q,n)/q^n denote the frequency of such elements.We show that there exists a constant c > 0 such thatnu(q, n) >= c / sqrt(log _q n) ,for all n, q >= 2and this is optimal up to a constant factor in that we show0.28477 = 1 / e [log_q n], for all n, q >= 2
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| Publisher |
Aarhus University
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| Date |
1997-06-14
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| Type |
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion |
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| Format |
application/pdf
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| Identifier |
https://tidsskrift.dk/brics/article/view/18970
10.7146/brics.v4i44.18970 |
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| Source |
BRICS Report Series; No 44 (1997): RS-44 On the Density of Normal Bases in Finite Fields
BRICS Report Series; Nr. 44 (1997): RS-44 On the Density of Normal Bases in Finite Fields 1601-5355 0909-0878 |
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| Language |
eng
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| Relation |
https://tidsskrift.dk/brics/article/view/18970/16609
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