Classification Algorithms for Codes and Designs
A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and
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Algorithms and Computation in Mathematics • Volume 15 Editors Arjeh M. Cohen Henri Cohen David Eisenbud Bernd Sturmfels
Petteri Kaski Patric R.J. Östergård
Classification Algorithms for Codes and Designs With 61 Figures and 30 Tables
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Authors
Petteri Kaski Department of Computer Science and Engineering Helsinki University of Technology P. O. Box 5400 2015 HUT, Helsinki Finland e-mail: [email protected]
Patric R.J. Östergård Department of Electrical and Communications, Engineering Helsinki University of Technology P.O. Box 3000 2015 HUT, Helsinki Finland e-mail: [email protected]
Library of Congress Control Number: 2005935445
Mathematics Subject Classification (2000): 05-02, 05Bxx, 05Cxx, 05E20, 51Exx, 68-02, 68Rxx, 94-02, 94Bxx
ISSN 1431-1550 ISBN-10 3-540-28990-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-28990-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
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Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Graphs, Designs, and Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Incidence Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 t-Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Balanced Incomplete Block Designs . . . . . . . . . . . . . . . . . . 2.2.4 Steiner Triple Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Some Ot
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