Cyclic Codes
In Section 4.5 we defined the automorphism group Aut(C) of a code C. Corresponding to this group there is a group of permutation matrices. Sometimes the definition of Aut(C) is extended by replacing permutation matrices by monomial matrices, i.e. matrices
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86
P. R. Halmos (Managing Editor)
J. H. van Lint
Introduction to Coding Theory With 8 Illustrations
Springer Science+Business Media, LLC
J. H. van Lint Eindhoven University of Technology Department of Mathematics Den Dolech 2, P.O. Box 513 5600 MB Eindhoven The Netherlands
Editorial Board P. R. Halmos
F. W. Gehring
c.
Managing Editor Indiana University Department of Mathematics Bloomington, IN 47401 U.S.A.
University of Michigan Department of Mathematics Ann Arbor, MI 48104 U.S.A.
University of California at Berkeley Department of Mathematics Berkeley, CA 94720 U.S.A.
C. Moore
AMS Classification (1980): 05-01, 68E99, 94A24
Library of Congress Cataloging in Publication Data Lint, Jacobus Hendricus van, 1932Introduction to coding theory. (Graduate texts for mathematics; 86) Bibliography: p. Includes index. 1. Coding theory. 1. Title. II. Series. QA268.L57 519.4 82-3242 AACR2
© 1982 by Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc. in 1982 Softcover reprint ofthe hardcover 1st edition 1982
All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer Science+Business Media, LLC
9 8 76 54 3 2 1 ISBN 978-3-662-08000-9 ISBN 978-3-662-07998-0 (eBook) DOI 10.1007/978-3-662-07998-0
Preface
Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathematicians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification and a little more history of the book are necessary. A few years ago it was remarked at a meeting on coding theory that there was no book available which could be used for an introductory course on coding theory (mainly for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M.C. Syllabus 31). The course, which was a great success, was given by M. R. Best, A. E. Brouwer, P. van Emde Boas, T. M. V. Janssen, H. W. Lenstra Jr., A. Schrijver, H. C. A. van Tilborg and myself. Since then the book has been used for a number of years at the Technological Universities of Delft and Eindhoven. The comments above explain why
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