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OverviewThis 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. Full Product DetailsAuthor: Igor ShparlinskiPublisher: Springer Imprint: Springer Edition: Softcover reprint of hardcover 1st ed. 1999 Volume: 477 Dimensions: Width: 16.00cm , Height: 2.70cm , Length: 24.00cm Weight: 0.932kg ISBN: 9789048152032ISBN 10: 9048152038 Pages: 528 Publication Date: 07 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsLinks 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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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