Overview

This is a survey of 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.

Full Product Details

Author:   Igor Shparlinski
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   477
Dimensions:   Width: 15.60cm , Height: 3.00cm , Length: 23.40cm
Weight:   2.060kg
ISBN:  

9780792356622

ISBN 10:   0792356624
Pages:   528
Publication Date:   31 May 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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 fur Mathematik, 132:1 (2001)

'...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 fur Mathematik, 132:1 (2001)

'...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 fur Mathematik, 132:1 (2001)

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