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- DescriptionFinite 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 ), or at the list of references in I. E. Shparlinski's book  (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 rmal 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  in 1888. Since rmal 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.
- Author(s)Dirk Hachenberger
- PublisherSpringer-Verlag New York Inc.
- Date of Publication08/10/2012
- Series TitleThe Springer International Series in Engineering and Computer Science
- Series Part/Volume Number390
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight296 g
- Width155 mm
- Height235 mm
- Spine10 mm
- Edition StatementSoftcover reprint of the original 1st ed. 1997
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