Finite Fields : Normal Bases and Completely Free Elements

Language: English

Published by Springer Us Jan 1997, 1997

0792398513 / 9780792398516

Series: Book 224 of 260 - The Springer International Series in Engineering and Computer Science

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Neuware - 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.

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Title
Finite Fields : Normal Bases and Completely Free Elements
Author
Dirk Hachenberger
Publisher
Springer Us Jan 1997
Publication year
1997
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0792398513
ISBN 13
9780792398516
Item weight
440 grams
Dimensions
234x156x13 mm
Series
Book 224 of 260: The Springer International Series in Engineering and Computer Science

AHA-BUCH GmbH

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