Finite Fields: Normal Bases and Completely Free Elements (The Springer International Series in Engineering and Computer Science, Band 390) - Softcover

Hachenberger, Dirk

Softcover

ISBN 10: 146137877X ISBN 13: 9781461378778

Verlag: Springer, 2012

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Dirk Hachenberger is a mathematician working in the fields of combinatorics, number theory, applicable algebra, finite geometry and coding theory. He is the recipient of the 2004 Hall medal of the Institute for Combinatorics and its Applications (ICA). He was also awarded the price for good teaching of the Bavarian State Minister for Science, Research and Arts in 2004. He has published the books "Finite Fields: Normal bases and completely free elements" (in English) and "Mathematics for computer scientists" (in German). Dieter Jungnickel is an internationally known mathematician working in the fields of applicable algebra, coding theory, design theory, finite geometry, combinatorics and combinatorial optimization. He is the recipient of the 2018 Euler medal of the Institute for Combinatorics and its Applications (ICA). He has published several well-known books, including "Design Theory", "Optimization Methods", "Finite fields: Structure and arithmetics", "CodingTheory", "Combinatorics" and "Graphs, Networks and Algorithms", some of which have been published both in English and German.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 146137877X
• ISBN 13: 9781461378778
• Einband: Taschenbuch
• Anzahl der Seiten: 188
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland