Characters and Cyclotomic Fields in Finite Geometry

✍ Scribed by Bernhard Schmidt (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2002
Tongue: English
Leaves: 106
Series: Lecture Notes in Mathematics 1797
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Introduction....Pages 1-25
2. The field descent....Pages 27-51
3. Exponent bounds....Pages 53-78
4. Two-weight irreducible cyclic codes....Pages 79-90
Bibliography....Pages 91-98
Index....Pages 99-100

✦ Subjects

Combinatorics

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