Finite Fields: Theory and Computation

Finite Fields: Theory and Computation

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.


Author
Publisher Springer Science & Business Media
Release Date
ISBN 9780792356622
Pages 560 pages
Finite Fields: Theory and Computation
Language: en
Pages: 560
Authors: Igor Shparlinski
Categories: Mathematics
Type: BOOK - Published: 1999-05-31 - Publisher: Springer Science & Business Media

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible
Arithmetic of Finite Fields
Language: en
Pages: 214
Authors: Joachim von zur Gathen
Categories: Computers
Type: BOOK - Published: 2008-06-25 - Publisher: Springer Science & Business Media

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Language: en
Pages: 271
Authors: Gary L. Mullen
Categories: Computers
Type: BOOK - Published: 2004-03-19 - Publisher: Springer Science & Business Media

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Language: en
Pages: 285
Authors: Pascale Charpin
Categories: Mathematics
Type: BOOK - Published: 2013-05-28 - Publisher: Walter de Gruyter

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Language: en
Pages: 1068
Authors: Gary L. Mullen
Categories: Computers
Type: BOOK - Published: 2013-06-17 - Publisher: CRC Press

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Language: en
Pages: 388
Authors: Zhe-Xian Wan
Categories: Mathematics
Type: BOOK - Published: 2011-09-13 - Publisher: World Scientific Publishing Company

A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer sc
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Language: en
Pages: 204
Authors: Michel Lavrauw
Categories: Mathematics
Type: BOOK - Published: 2012 - Publisher: American Mathematical Soc.

This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgiu
Finite Fields
Language: en
Pages: 384
Authors: Gary McGuire
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: American Mathematical Soc.

This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes sur
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Language: en
Pages: 354
Authors: Kai-Uwe Schmidt
Categories: Mathematics
Type: BOOK - Published: 2019-07-08 - Publisher: Walter de Gruyter GmbH & Co KG

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, a
Lectures on Finite Fields and Galois Rings
Language: en
Pages: 352
Authors: Zhe-Xian Wan
Categories:
Type: BOOK - Published: 2003-08-12 - Publisher: World Scientific Publishing Company

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explici