Generalizations of the Normal Basis Theorem of Finite Fields

1990 ◽  
Vol 3 (3) ◽  
pp. 330-337 ◽  
Author(s):  
Nader H. Bshouty ◽  
Gadiel Seroussi
Keyword(s):  
Finite Fields ◽  
Normal Basis ◽  
Basis Theorem

The Normal Basis Theorem

1979 ◽  
Vol 86 (3) ◽  
pp. 212-212
Author(s):  
William C. Waterhouse
Keyword(s):  
Normal Basis ◽  
Basis Theorem

The Normal Basis Theorem

1950 ◽  
Vol s1-25 (4) ◽  
pp. 259-264 ◽  
Author(s):  
J. W. S. Cassels ◽  
G. E. Wall
Keyword(s):  
Normal Basis ◽  
Basis Theorem

The Normal Basis Theorem

1979 ◽  
Vol 86 (3) ◽  
pp. 212 ◽  
Author(s):  
William C. Waterhouse
Keyword(s):  
Normal Basis ◽  
Basis Theorem

scholarly journals CONSTRUCTION OF SELF-DUAL INTEGRAL NORMAL BASES IN ABELIAN EXTENSIONS OF FINITE AND LOCAL FIELDS

2010 ◽  
Vol 06 (07) ◽  
pp. 1565-1588 ◽  
Author(s):  
ERIK JARL PICKETT
Keyword(s):  
Galois Group ◽  
Finite Fields ◽  
Galois Extension ◽  
Valuation Ring ◽  
Finite Extension ◽  
Normal Basis ◽  
Local Fields ◽  
Abelian Extensions ◽  
Construction Of Self ◽  
Odd Degree

Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that Tr F/E(g(x), h(x)) = δg, h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char (E) ≠ 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char (E) = 2, then F admits a self-dual normal basis if and only if the exponent of Γ is not divisible by 4. In this paper, we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let K be a finite extension of ℚp, let L/K be a finite abelian Galois extension of odd degree and let [Formula: see text] be the valuation ring of L. We define AL/K to be the unique fractional [Formula: see text]-ideal with square equal to the inverse different of L/K. It is known that a self-dual integral normal basis exists for AL/K if and only if L/K is weakly ramified. Assuming p ≠ 2, we construct such bases whenever they exist.

scholarly journals The strong primitive normal basis theorem

2010 ◽  
Vol 143 (4) ◽  
pp. 299-332 ◽  
Author(s):  
Stephen D. Cohen ◽  
Sophie Huczynska
Keyword(s):  
Normal Basis ◽  
Basis Theorem

A Proof of the Normal Basis Theorem

1975 ◽  
Vol 82 (9) ◽  
pp. 915-918 ◽  
Author(s):  
T. R. Berger ◽  
I. Reiner
Keyword(s):  
Normal Basis ◽  
Basis Theorem

THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER

2003 ◽  
Vol 67 (01) ◽  
pp. 41-56 ◽  
Author(s):  
STEPHEN D. COHEN ◽  
SOPHIE HUCZYNSKA
Keyword(s):  
Normal Basis ◽  
Basis Theorem

scholarly journals Cohomology and the normal basis theorem

2007 ◽  
Vol 18 (1) ◽  
pp. 69-72
Author(s):  
Patrik Lundstrfim
Keyword(s):  
Normal Basis ◽  
Basis Theorem
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