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The Springer International Series in Engineering and Computer Science

Finite Fields

Normal Bases and Completely Free Elements

Authors: Hachenberger, Dirk

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  • ISBN 978-1-4615-6269-6
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About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 106,99 €
price for Spain (gross)
  • ISBN 978-1-4615-6269-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 166,35 €
price for Spain (gross)
  • ISBN 978-0-7923-9851-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 135,19 €
price for Spain (gross)
  • ISBN 978-1-4613-7877-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Finite Fields
Book Subtitle
Normal Bases and Completely Free Elements
Authors
Series Title
The Springer International Series in Engineering and Computer Science
Series Volume
390
Copyright
1997
Publisher
Springer US
Copyright Holder
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
Series ISSN
0893-3405
Edition Number
1
Number of Pages
XII, 171
Topics