Applications of Algebra to Communications, Control, and Signal Processing
Over the last 50 years there have been an increasing number of applications of algebraic tools to solve problems in communications, in particular in the fields of error-control codes and cryptography. More recently, broader applications have emerged, requ
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Series Editors Stan Zdonik Peng Ning Shashi Shekhar Jonathan Katz Xindong Wu Lakhmi C. Jain David Padua Xuemin Shen Borko Furht VS Subrahmanian Martial Hebert Katsushi Ikeuchi Bruno Siciliano
For further volumes: http://www.springer.com/series/10028
Nigel Boston
Applications of Algebra to Communications, Control, and Signal Processing
Nigel Boston University of Wisconsin Madison, WI, USA
ISSN 2191-5768 ISSN 2191-5776 (electronic) ISBN 978-1-4614-3862-5 ISBN 978-1-4614-3863-2 (eBook) DOI 10.1007/978-1-4614-3863-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012935583 © The Author 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This book is dedicated to my wife, Susan Ann Boston.
Preface
Over the years, engineers and computer scientists have increasingly begun to use mathematical tools. Currently, it is standard for students in these fields to learn some complex analysis, probability, and statistics. There has, however, been a quietly growing introduction of tools from abstract algebra. Traditionally these have been used mostly in coding theory and cryptography, but there are emerging new areas of application for abstract algebra. For example, the first Applied Algebra Days conference, co-organized by the author and
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