Characters and Cyclotomic Fields in Finite Geometry

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 substanti

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2. Manuscripts should be submitted (preferably in duplicate) either to one of the series editors or to Springer-Verlag, Heidelberg. In general, manuscripts will be sent out to 2 external referees for evaluation. If a decision cannot yet be reached on the basis of the first 2 reports, further referees may be contacted: the author will be informed of this. A final decision to publish can be made only on the basis of the complete manuscript, however a refereeing process leading to a preliminary decision can be based on a pre-final or incomplete manuscript. The strict minimum amount of material that will be considered should include a detailed outline describing the planned contents of each chapter, a bibliography and several sample chapters. Authors should be aware that incomplete or insufficiently close to final manuscripts almost always result in longer refereeing times and nevertheless unclear referees' recommendations, making further refereeing of a final draft necessary. Authors should also be aware that parallel submission of their manuscript to another publisher while under consideration for LNM will in general lead to immediate rejection. 3. Manuscripts should in general be submitted in English. Final manuscripts should contain at least 100 pages of mathematical text and should include - a table of contents: - an informative introduction, with adequate motivation and perhaps some historical remarks: it should be accessible to a reader not intimately familiar with the topic treated; - a subject index: as a rule this is genuinely helpful for the reader.

Continued on inside back-cover

Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris

1797

3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo

Bernhard Schmidt

Characters and Cyclotomic Fields in Finite Geometry

13

Author Bernhard Schmidt Institut für Mathematik Universität Augsburg Universitätsstrasse 14 86135 Augsburg, Germany E-mail: [email protected]

Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek - CIP-Einheitsaufnahme Schmidt, Bernhard: Characters and cyclotomic fields in finite geometry / Bernhard Schmidt. Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in mathematics ; 1797) ISBN 3-540-44243-X

Mathematics Subject Classification (2000): 05B10, 05B20, 05B25 ISSN 0075-8434 ISBN 3-540-44243-x Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the Germa