Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography by Igor ShparlinskiFinite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography by Igor Shparlinski

Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding…

byIgor Shparlinski

Paperback | December 7, 2010

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This book provides an exhaustive survey of the most recent achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography. Topics treated include polynomial factorization over finite fields, the finding and distribution of irreducible primitive and other special polynomials, constructing special bases of extensions of finite fields, curves and exponential sums, and linear recurrent sequences. Besides a general overview of the area, its results and methods, it suggests a number of interesting research problems of various levels of difficulty. The volume concludes with an impressive bibliographical section containing more than 2300 references. Audience: This work will be of interest to graduate students and researchers in field theory and polynomials, number theory, symbolic computation, symbolic/algebraic manipulation, and coding theory.

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Title:Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding…Format:PaperbackDimensions:542 pages, 9.45 × 6.3 × 0 inPublished:December 7, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048152038

ISBN - 13:9789048152032

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Table of Contents

Preface. Acknowledgments. Notation. Introduction. Links flowchart. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrence Sequences in Finite Fields and Cyclic Linear Codes. 8. Finite Fields and Discrete Mathematics. 9. Congruences. 10. Some Related Problems. Appendix 1. Appendix 2. Appendix 3. References. Index.

Editorial Reviews

`...the book can yet be highly recommended as encyclopaedia on these topics, in particular because many Russian papers are incorporated which are hardly accessible.' Monatschafte für Mathematik, 132:1 (2001)