The Springer International Series in Engineering and Computer Science

Finite Fields

Normal Bases and Completely Free Elements

Autoren: Hachenberger, Dirk

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Über dieses Buch

Finite Fields are fundamental structures of Discrete Mathematics. They serve as basic data structures in pure disciplines like Finite Geometries and Combinatorics, and also have aroused much interest in applied disciplines like Coding Theory and Cryptography. A look at the topics of the proceed­ ings volume of the Third International Conference on Finite Fields and Their Applications (Glasgow, 1995) (see [18]), or at the list of references in I. E. Shparlinski's book [47] (a recent extensive survey on the Theory of Finite Fields with particular emphasis on computational aspects), shows that the area of Finite Fields goes through a tremendous development. The central topic of the present text is the famous Normal Basis Theo­ rem, a classical result from field theory, stating that in every finite dimen­ sional Galois extension E over F there exists an element w whose conjugates under the Galois group of E over F form an F-basis of E (i. e. , a normal basis of E over F; w is called free in E over F). For finite fields, the Nor­ mal Basis Theorem has first been proved by K. Hensel [19] in 1888. Since normal bases in finite fields in the last two decades have been proved to be very useful for doing arithmetic computations, at present, the algorithmic and explicit construction of (particular) such bases has become one of the major research topics in Finite Field Theory.

Inhaltsverzeichnis (6 Kapitel)

Inhaltsverzeichnis (6 Kapitel)

Dieses Buch kaufen

eBook 106,99 €
Preis für Deutschland (Brutto)
  • ISBN 978-1-4615-6269-6
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 171,15 €
Preis für Deutschland (Brutto)
Softcover 139,09 €
Preis für Deutschland (Brutto)
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Bibliografische Information

Bibliographic Information
Buchtitel
Finite Fields
Buchuntertitel
Normal Bases and Completely Free Elements
Autoren
Titel der Buchreihe
The Springer International Series in Engineering and Computer Science
Buchreihen Band
390
Copyright
1997
Verlag
Springer US
Copyright Inhaber
Springer Science+Business Media New York
eBook ISBN
978-1-4615-6269-6
DOI
10.1007/978-1-4615-6269-6
Hardcover ISBN
978-0-7923-9851-6
Softcover ISBN
978-1-4613-7877-8
Buchreihen ISSN
0893-3405
Auflage
1
Seitenzahl
XII, 171
Themen