Overview

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.

Full Product Details

Author:   Gary L. Mullen (Pennsylvania State University, University Park, USA) ,  Daniel Panario (Carleton University, Ottawa, Ontario, Canada)
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Volume:   78
Dimensions:   Width: 17.80cm , Height: 5.60cm , Length: 25.40cm
Weight:   1.814kg
ISBN:  

9781439873786

ISBN 10:   143987378
Pages:   1070
Publication Date:   17 June 2013
Audience:   Professional and scholarly ,  General/trade ,  Professional & Vocational ,  General
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

INTRODUCTION: History of Finite Fields. Introduction to Finite Fields. THEORETICAL PROPERTIES: Irreducible Polynomials. Primitive Polynomials. Bases. Exponential and Character Sums. Equations over Finite Fields. Permutation Polynomials. Special Functions over Finite Fields. Sequences over Finite Fields. Algorithms. Curves over Finite Fields. Miscellaneous Theoretical Topics. APPLICATIONS: Combinatorial. Algebraic Coding Theory. Cryptography. Miscellaneous Applications. Bibliography. Index.

Reviews

... a brilliant, monumental work on the state of the art in theory and applications of finite fields. It's a must for everyone doing research in finite fields and their related areas. ... It presents such a huge amount of information readily available and masterly presented. Editors, contributors, and the publisher are equally congratulated for providing such a beautiful result not only for the finite field community, but also for those from the applied areas, especially cryptographers and coding theorists. -Olaf Ninnemann, Berlin, in Zentralblatt MATH 1319 The handbook will be very useful for senior-level students, teachers, and researchers in mathematics and computer science. It will also be useful for scientists, engineers, and practitioners. The handbook is well organized. ... It is likely to become a standard reference book for the theory and applications of finite fields. ... It will be a very useful addition to the libraries of academic and research institutions. -S.V.Nagaraj, Chennai, India, in SIGACT News

... a brilliant, monumental work on the state of the art in theory and applications of finite fields. It's a must for everyone doing research in finite fields and their related areas. ... It presents such a huge amount of information readily available and masterly presented. Editors, contributors, and the publisher are equally congratulated for providing such a beautiful result not only for the finite field community, but also for those from the applied areas, especially cryptographers and coding theorists. -Olaf Ninnemann, Berlin, in Zentralblatt MATH 1319 The handbook will be very useful for senior-level students, teachers, and researchers in mathematics and computer science. It will also be useful for scientists, engineers, and practitioners. The handbook is well organized. ... It is likely to become a standard reference book for the theory and applications of finite fields. ... It will be a very useful addition to the libraries of academic and research institutions. -S.V.Nagaraj, Chennai, India, in SIGACT News

Author Information

Gary L. Mullen is a professor of mathematics at The Pennsylvania State University. Daniel Panario is a professor of mathematics at Carleton University.

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