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.

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Bibliographic Information

Book Title: Characters and Cyclotomic Fields in Finite Geometry
Authors: Bernhard Schmidt
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b84213
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2002
Softcover ISBN: 978-3-540-44243-1Published: 23 October 2002
eBook ISBN: 978-3-540-45797-8Published: 13 October 2004
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 108
Topics: Combinatorics

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Table of contents (6 chapters)

Front Matter

1. Introduction

2. The field descent

3. Exponent bounds

4. Two-weight irreducible cyclic codes

Bibliography

Index

Back Matter

About this book