Title: Finite Fields: Normal Bases and Completely Free Elements (The Springer International Series in Engineering and Computer Science, 390)
Publisher: Springer
Publication Date: 1997
Language: English
ISBN 10: 0792398513
ISBN 13: 9780792398516
Binding: Hardcover
Condition: New

About this title

Synopsis

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.

Product Description

Finite Fields Over the years, normal bases in finite fields have been proved to be very useful for doing arithmetic computations. In addition to interest in arbitrary normal bases, this book examines a special class of normal bases whose existence has only been settled more recently. It serves as a reference for researchers in finite fields.

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