Coding Theory and Design Theory

Part I Coding Theory

  • Dijen Ray-Chaudhuri
Conference proceedings

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. E. F. Assmus Jr., J. D. Key
    Pages 1-8
  3. Richard A. Brualdi, Vera S. Pless
    Pages 9-15
  4. Richard Clayton
    Pages 51-64
  5. Zongduo Dai, Xuning Feng, Mulan Liu, Zhe-Xian Wan
    Pages 65-71
  6. Michel Marie Deza, Komei Fukuda
    Pages 72-92
  7. M. Deza, D. K. Ray-Chaudhuri, N. M. Singhi
    Pages 93-101
  8. Willard L. Eastman
    Pages 113-127
  9. Marshall Hall Jr.
    Pages 128-136
  10. Jacobus H. Van Lint
    Pages 137-162
  11. Jonathan D. H. Smith
    Pages 163-187
  12. Patrick Solé
    Pages 188-192
  13. Paul Terwilliger
    Pages 193-212
  14. G. R. Vijayakumar, N. M. Singhi
    Pages 213-218

About these proceedings

Introduction

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".

Keywords

Combinatorics algorithms coding theory communication graphs

Authors and affiliations

  • Dijen Ray-Chaudhuri
    • 1
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8994-1
  • Copyright Information Springer-Verlag New York 1990
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8996-5
  • Online ISBN 978-1-4613-8994-1
  • Series Print ISSN 0940-6573
  • About this book