Characters and Cyclotomic Fields in Finite Geometry

  • Authors
  • Bernhard Schmidt

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

Introduction

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.

Keywords

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

Bibliographic information

  • DOI https://doi.org/10.1007/b84213
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44243-1
  • Online ISBN 978-3-540-45797-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book