A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Explicit Iterative Constructions of Normal Bases and Completely Free Elements in Finite Fields

1996
*
Finite Fields and Their Applications
*

A characterization of

doi:10.1006/ffta.1996.0001
fatcat:smmdbtjtrnh23g35b5c627nhey
*normal**bases*and complete*normal**bases**in*GF(q r n ) over GF(q), where q Ͼ 1 is any prime power, r is any prime number different from the characteristic of GF(q), and n Ն 1 is any ... Such a basis is called a*normal*basis*in*GF(q m ) over GF(q). ... So, we are able to iteratively find*normal**bases*or complete*normal**bases**in*any*finite*subfield of GF(q r ȍ ) over GF(q), if we can solve the following main problem. Problem 2.6. ...##
###
CONSTRUCTION OF SELF-DUAL INTEGRAL NORMAL BASES IN ABELIAN EXTENSIONS OF FINITE AND LOCAL FIELDS

2010
*
International Journal of Number Theory
*

*In*this paper we

*construct*self-dual

*normal*basis generators for

*finite*extensions of

*finite*

*fields*whenever they exist. ... It is known that a self-dual integral

*normal*basis exists for A_L/K if and only if L/K is weakly ramified. Assuming p≠ 2, we

*construct*such

*bases*whenever they exist. ...

*Finite*

*Fields*

*In*this section we describe how to

*construct*self-dual

*normal*

*bases*for any

*finite*extension of a

*finite*

*field*for which they exist. ...

##
###
Page 1556 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

Summary: “GauB periods have been used successfully as a tool for

*constructing**normal**bases**in**finite**fields*. ... Since*normal**bases**in**finite**fields*have been proved*in*the last two decades to be very useful for doing arithmetic computations, the algorithmic and explicit*construction*of (certain) such*bases*has become ...##
###
Page 3702 of Mathematical Reviews Vol. , Issue 94g
[page]

1994
*
Mathematical Reviews
*

*Normal*

*bases*; 4. Dual

*bases*; 5.

*Normal*

*bases*and duality; 6. Shift register sequences; 7. Characters and Gaussian sums. ... The book emphasizes the

*constructive*and computational sides of

*finite*

*field*theory, and is divided into the following seven chapters: 1. Basic results; 2. Explicit

*construction*of

*finite*

*fields*; 3. ...

##
###
Page 4606 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

The aim of the paper is to

*construct*self-complementary*normal*’ 11 NUMBER THEORY 4606*bases*, also called self-dual*normal**bases*,*in**finite**fields*with characteristic 2. ...*In*the second part the author*constructs*a self-complementary*normal*basis over GF(q), where g = 2’, with the help of a*normal*basis B*in*GF(q"). ...##
###
Finite field arithmetic using quasi-normal bases

2007
*
Finite Fields and Their Applications
*

For some extension

doi:10.1016/j.ffa.2006.09.008
fatcat:6pm54fwepfbv5ku52j3q53jsc4
*fields*F q n over F q , we*construct*quasi-*normal**bases*of low density. ... Efficient multiplication*in**finite**fields*F q n requires F q -*bases*of low density, i.e., such that the products of the basis elements have a sparse expression*in*the basis. ... They are a new family of F q -*bases*of*finite**field*F q n which generalizes the notion of*normal**bases*. ...##
###
A proper base change theorem for non-torsion sheaves in étale cohomology

1988
*
Journal of Pure and Applied Algebra
*

We show that under certain additional hypotheses the proper

doi:10.1016/0022-4049(88)90102-8
fatcat:6n765dntjbfd3nfdzywtd5ey4q
*base*change theorem holds for arbitrary abelian sheaves. ... abelian group and r: Y* Y is a*finite*morphism with Y*normal*. ...*In*particular this is the case for the proper*base*change theorem as is shown by the example*in*[l, XII, 21. ...##
###
The gamma construction and asymptotic invariants of line bundles over arbitrary fields
[article]

2019
*
arXiv
*
pre-print

To do so over imperfect

arXiv:1809.01217v3
fatcat:wcaeoon4wvbyvdyjm32vz5ram4
*fields*, we prove a scheme-theoretic version of the gamma*construction*of Hochster and Huneke to reduce to the setting where the ground*field*is F-*finite*. ... We also extend Nakayama's description of the restricted*base*locus to klt or strongly F-regular varieties over arbitrary*fields*. ... Since k(x 1/p ∞ ) contains the infinite perfect*field*F p (x 1/p ∞ ) and applying the gamma*construction*to k(x 1/p ∞ ) results*in*an F -*finite**field*(*Construction*3.1 and Lemma 3.2(i)), it therefore suffices ...##
###
Page 99 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

If F = GF(q) is a

*finite**field*and n > | an integer, then it is one of the major problems*in*the theory of*finite**fields*to (explicitly)*construct*an irreducible polynomial of degree n over F (possibly ... Dirk Hachenberger (D-AGSB-MI; Augsburg) 98a:11172 11T06 Chapman, Robin (4-EXTR; Exeter) Completely*normal*elements*in*iterated quadratic extensions of*finite**fields*. ...##
###
Page 3841 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

For similar values of n and q, self-dual

*normal**bases*are also*constructed*and these too can have complexity 3n — 2 when n = p, the novel feature here being*constructibility*. ... “optimal*normal**bases*” [see X. ...##
###
Normal high order elements in finite field extensions based on the cyclotomic polynomials

2020
*
Algebra and discrete mathematics
*

We consider elements which are both of high multiplicative order and

doi:10.12958/adm1117
fatcat:jbvkgochgrcjxig2gpmlvqnxci
*normal**in*extensions F q m of the*field*F q . ... If the extension is defined by a cyclotomic polynomial, we*construct*such elements explicitly and give explicit lower bounds on their orders. 2010 MSC: 11T30. ... The current paper enriches the list of*normal*high order elements*in**finite**field*extensions*based*on cyclotomic polynomials. ...##
###
Construction of Irreducible Polynomials in Galois elds, GF(2m) Using Normal Bases

2019
*
Asian Research Journal of Mathematics
*

This thesis is about

doi:10.9734/arjom/2019/v14i330131
fatcat:ip2oqqrdrjd6ddo5iry237stpm
*Construction*of Polynomials*in*Galois*fields*Using*Normal**Bases**in**finite**fields*. ... We found the actual*construction*of polynomials*in*GF(2m) with degree less than or equal to m − 1 and also illustrated how this*construction*can be done using*normal**bases*. ... Acknowledgement The authors are grateful to the referees for their careful reading,*constructive*criticisms, comments and suggestions, which have helped us to improve this work significantly. ...##
###
MODIFIED CHANGE-OF-BASIS CONVERSION METHOD IN GF(2m)

2020
*
Radìoelektronika, Ìnformatika, Upravlìnnâ
*

The subject of the study is the methods and algorithms for calculations

doi:10.15588/1607-3274-2020-2-12
fatcat:42mt3dujwrdedd7ealnsonkwru
*in*the Galois*fields**in*polynomial and*normal**bases*. Objective. ... the conversion between*bases*of binary*fields*gives an increase*in*speed over 15 times for the parameter m > 14; the proposed approach for*constructing*a conversion matrix gives an increase*in*the speed ... It can be implemented by the*construction*of digital filters that are*based*on computations*in**finite**fields*. ...##
###
Book Review: Computational and algorithmic problems in finite fields

1994
*
Bulletin of the American Mathematical Society
*

It is an excellent textbook and reference for people interested

doi:10.1090/s0273-0979-1994-00466-5
fatcat:lpl6spoff5b7hop6pbbrlxhxsa
*in**normal**bases*and*in*the applications of*finite**fields*to combinatorics. ... Therefore, they should be of interest to mathematicians working on areas related to*finite**fields*. Jungnickel's book essentially focuses on*normal**bases**in**finite**fields*, namely, a basis of F? ...##
###
Page 6790 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

Included too is an application to the existence of trace-compatible sequences of primitive

*normal**bases*for certain primary closures of Galois*fields*. S. D. ... Let K be a*field*and F a*finite*Galois extension of K with Ga- lois group G. ...
« Previous

*Showing results 1 — 15 out of 565,409 results*