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Finite Fields : Normal Bases and Completely Free Elements :  Normal Bases and Completely Free Elements - Dirk Hachenberger

Finite Fields : Normal Bases and Completely Free Elements

Normal Bases and Completely Free Elements

Hardcover Published: December 2009
ISBN: 9780792398516
Number Of Pages: 171

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The central topic of Finite Fields: Normal Bases and Completely Free Elements is the famous Normal Basis Theorem, a classical result from field theory. In the last two decades, normal bases in finite fields have been proved to be very useful for doing arithmetic computations. At present, the algorithmic and explicit construction of such bases has become one of the major research topics in Finite Field Theory. Moreover, the search for such bases also led to a better theoretical understanding of the structure of finite fields. In addition to interest in arbitrary normal bases, Finite Fields: Normal Bases and Completely Free Elements examines a special class of normal bases whose existence has only been settled more recently. The main problems considered in the present work are the characterization, the enumeration, and the explicit construction of completely free elements in arbitrary finite dimensional extensions over finite fields. Up to now, there is no work done stating whether the universal property of a completely free element can be used to accelerate arithmetic computations in finite fields. Therefore, the present work belongs to Constructive Algebra and constitutes a contribution to the theory of Finite Fields. This book serves as an excellent reference for researchers in finite fields, and may be used as a text for advanced courses on the subject.

Preface
Introduction and Outlinep. 1
Module Structures in Finite Fieldsp. 37
Simultaneous Module Structuresp. 61
The Existence of Completely Free Elementsp. 75
A Decomposition Theoryp. 99
Explicit Constructionsp. 127
Referencesp. 161
List of Symbolsp. 165
Indexp. 169
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792398516
ISBN-10: 0792398513
Series: The Springer International Series in Engineering and Computer Science
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 171
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.27
Weight (kg): 0.98