A deterministic construction for normal bases of abelian extensions

1994 ◽  
Vol 22 (12) ◽  
pp. 4751-4757 ◽  
Author(s):  
A. Poli
Keyword(s):  
Normal Bases ◽  
Abelian Extensions ◽  
Deterministic Construction

scholarly journals A valuation criterion for normal bases in elementary abelian extensions

2007 ◽  
Vol 39 (5) ◽  
pp. 705-708 ◽  
Author(s):  
Nigel P. Byott ◽  
G. Griffith Elder
Keyword(s):  
Normal Bases ◽  
Abelian Extensions

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

Optimal Normal Bases

1993 ◽  
pp. 93-114
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Normal Bases

Normal Bases

1993 ◽  
pp. 69-92
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Normal Bases

Optimal normal bases

1992 ◽  
Vol 2 (4) ◽  
pp. 315-323 ◽  
Author(s):  
Shuhong Gao ◽  
Hendrik W. Lenstra
Keyword(s):  
Normal Bases
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