Cyclic Difference Sets
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182 Leonard D. Baumert California Institute of Technology Pasadena, CA / USA
Cyclic Difference Sets
Springer-Verlag Berlin · Heidelberg . NewYork 1971
Lecture Notes in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich
182 Leonard D. Baumert California Institute of Technology Pasadena, CA / USA
Cyclic Difference Sets
Springer-Verlag Berlin · Heidelberg . NewYork 1971
ISBN 3-540-05368-9 Springer-Verlag Berlin' Heidelberg· New York ISBN 0-387-05368-9 Springer-Verlag New York· Heidelberg· Berlin This work is subject to copyright, All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1971. Library of Congress Catalog Card Number 73-153466 Printed in Germany. Offsetdruck: Julius Beltz, Weinheim/Bergstr.
CYCLIC DIFFERENCE SETS
A fairly comprehensive survey of the general theory of cyclic difference sets is given below.
The aim of chis survey is to provide a cohesive presentation of
the known facts as well as an introduction to some of the outstanding problems. The more general topics of block designs and difference sets in finite groups are introduced but only those aspects of these subjects which shed some light on problems arising for cyclic difference sets are developed. It is not expected that many will wish to read this survey sequentially from the beginning.
For this reason the chapters and to a lesser degree the sections
within them are largely independent of each other, having been written that way in order to encourage the reader to skip around and follow his own interests.
However
a certain familiarity with the contents of Chapter I is presupposed elsewhere. Beyond this, interconnections between the various sections and chapters are indicated when they seem relevant.
This structure, coupled with the aim of making the
later material understandable to as many as possible, has led to the anomaly that, in some cases, quite elementary concepts are defined in the later chapters, whereas these same concepts,
and a great deal more, were presupposed in earlier sections.
In addition to the specific references inserted in the text, the books of Marshall Hall, Jr., "Combinatorial Theory", Blaisdell Publishing Company, 1967, of H. B. Mann, "Addition Theorems", Interscience Publishers, 1965, and of H. J. Ryser, "Combinatorial Mathematics", Carus Mathematical Monograph No. 14, 1963, may be used as general references for a large part of this material. This survey was compiled in connection with research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7100, sponsored
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