The IMA Volumes in Mathematics and its Applications

Coding Theory and Design Theory

Part I Coding Theory

Editors: Ray-Chaudhuri, Dijen (Ed.)

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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".

Table of contents (17 chapters)

Table of contents (17 chapters)
  • Baer Subplanes, Ovals and Unitals

    Assmus, E. F., Jr. (et al.)

    Pages 1-8

  • On the Length of Codes with a Given Covering Radius

    Brualdi, Richard A. (et al.)

    Pages 9-15

  • The Differential Encoding of Coset Codes by Algebraic Methods

    Calderbank, A. R.

    Pages 16-34

  • 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

    Chakravarti, I. M.

    Pages 35-50

  • Perfect Multiple Coverings in Metric Schemes

    Clayton, Richard

    Pages 51-64

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4613-8994-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.99
price for USA in USD
  • ISBN 978-1-4613-8996-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Coding Theory and Design Theory
Book Subtitle
Part I Coding Theory
Editors
  • Dijen Ray-Chaudhuri
Series Title
The IMA Volumes in Mathematics and its Applications
Series Volume
20
Copyright
1990
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4613-8994-1
DOI
10.1007/978-1-4613-8994-1
Softcover ISBN
978-1-4613-8996-5
Series ISSN
0940-6573
Edition Number
1
Number of Pages
XIV, 239
Topics