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Finite Fields for Computer Scientists and Engineers

  • Book
  • © 1987

Overview

Authors:
  1. Robert J. McEliece

    1. California Institute of Technology, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Prologue

    • Robert J. McEliece
    Pages 1-2

  3. Euclidean Domains and Euclid’s Algorithm

    • Robert J. McEliece
    Pages 3-12

  4. Unique Factorization in Euclidean Domains

    • Robert J. McEliece
    Pages 13-18

  5. Building Fields from Euclidean Domains

    • Robert J. McEliece
    Pages 19-28

  6. Abstract Properties of Finite Fields

    • Robert J. McEliece
    Pages 29-53

  7. Finite Fields Exist and are Unique

    • Robert J. McEliece
    Pages 55-73

  8. Factoring Polynomials over Finite Fields

    • Robert J. McEliece
    Pages 75-96

  9. Trace, Norm, and Bit-Serial Multiplication

    • Robert J. McEliece
    Pages 97-121

  10. Linear Recurrences over Finite Fields

    • Robert J. McEliece
    Pages 123-149

  11. The Theory of m-Sequences

    • Robert J. McEliece
    Pages 151-167

  12. Crosscorrelation Properties of m-Sequences

    • Robert J. McEliece
    Pages 169-200

  13. Back Matter

    Pages 201-207
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Keywords

About this book

This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ­ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond­ ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char­ acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.

Authors and Affiliations

  • California Institute of Technology, USA

    Robert J. McEliece

Bibliographic Information

  • Book Title: Finite Fields for Computer Scientists and Engineers

  • Authors: Robert J. McEliece

  • Series Title: The Springer International Series in Engineering and Computer Science

  • DOI: https://doi.org/10.1007/978-1-4613-1983-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Kluwer Academic Publishers 1987

  • Hardcover ISBN: 978-0-89838-191-7Published: 30 November 1986

  • Softcover ISBN: 978-1-4612-9185-5Published: 17 September 2011

  • eBook ISBN: 978-1-4613-1983-2Published: 06 December 2012

  • Series ISSN: 0893-3405

  • Edition Number: 1

  • Number of Pages: XII, 208

  • Topics: Electrical Engineering, Algebra

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