© 2002

Characters and Cyclotomic Fields in Finite Geometry

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1797)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Bernhard Schmidt
    Pages 1-25
  3. Bernhard Schmidt
    Pages 27-51
  4. Bernhard Schmidt
    Pages 53-78
  5. Bernhard Schmidt
    Pages 79-90
  6. Bernhard Schmidt
    Pages 91-98
  7. Bernhard Schmidt
    Pages 99-100
  8. Back Matter
    Pages 101-105

About this book


This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.


Barker sequences Circulant Hadamard matrices Differences sets finite geometry irreducible cyclic codes

Bibliographic information

  • Book Title Characters and Cyclotomic Fields in Finite Geometry
  • Authors Bernhard Schmidt
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-44243-1
  • eBook ISBN 978-3-540-45797-8
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 108
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
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