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Coding Theory and Design Theory

Part I Coding Theory

  • Conference proceedings
  • © 1990

Overview

Authors:
  1. Dijen Ray-Chaudhuri

    1. Department of Mathematics, Ohio State University, Columbus, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 20)

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Table of contents (17 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Baer Subplanes, Ovals and Unitals

    • E. F. Assmus Jr., J. D. Key
    Pages 1-8

  3. On the Length of Codes with a Given Covering Radius

    • Richard A. Brualdi, Vera S. Pless
    Pages 9-15

  4. The Differential Encoding of Coset Codes by Algebraic Methods

    • A. R. Calderbank
    Pages 16-34

  5. Families of Codes with Few Distinct Weights from Singular and Non-Singular Hermitian Varieties and Quadrics in Projective Geometries and Hadamard Difference Sets and Designs Associated with Two-Weight Codes

    • I. M. Chakravarti
    Pages 35-50

  6. Perfect Multiple Coverings in Metric Schemes

    • Richard Clayton
    Pages 51-64

  7. Nonlinear Feedforward Sequences of m-Sequences II

    • Zongduo Dai, Xuning Feng, Mulan Liu, Zhe-Xian Wan
    Pages 65-71

  8. Loops of Clutters

    • Michel Marie Deza, Komei Fukuda
    Pages 72-92

  9. Positive Independence and Enumeration of Codes with a Given Distance Pattern

    • M. Deza, D. K. Ray-Chaudhuri, N. M. Singhi
    Pages 93-101

  10. Bounds on the Number of Pairs of Unjoined Points in a Partial Plane

    • David A. Drake, Paul Erdös
    Pages 102-112

  11. Inside Euclid’s Algorithm

    • Willard L. Eastman
    Pages 113-127

  12. Construction of Designs

    • Marshall Hall Jr.
    Pages 128-136

  13. Algebraic Geometric Codes

    • Jacobus H. Van Lint
    Pages 137-162

  14. Combinatorial Characters of Quasigroups

    • Jonathan D. H. Smith
    Pages 163-187

  15. Self-Dual Codes and Self-Dual Designs

    • Patrick Solé
    Pages 188-192

  16. The Incidence Algebra of a Uniform Poset

    • Paul Terwilliger
    Pages 193-212

  17. Some Recent Results on Signed Graphs with Least Eigenvalues ≥ -2

    • G. R. Vijayakumar, N. M. Singhi
    Pages 213-218

  18. Self-Orthogonal Codes and the Topology of Spinor Groups

    • Jay A. Wood
    Pages 219-239
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Keywords

About this book

This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year­ long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa­ per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge­ braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".

Authors and Affiliations

  • Department of Mathematics, Ohio State University, Columbus, USA

    Dijen Ray-Chaudhuri

Bibliographic Information

  • Book Title: Coding Theory and Design Theory

  • Book Subtitle: Part I Coding Theory

  • Authors: Dijen Ray-Chaudhuri

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4613-8994-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1990

  • Softcover ISBN: 978-1-4613-8996-5Published: 08 November 2011

  • eBook ISBN: 978-1-4613-8994-1Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: XIV, 239

  • Topics: Combinatorics

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