Algebraic Coding Theory Over Finite Commutative Rings
This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject.Coding theory has its origins in the engineering problem of effective electronic commu
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Steven T. Dougherty
Algebraic Coding Theory Over Finite Commutative Rings 123
SpringerBriefs in Mathematics Series Editors Nicola Bellomo Michele Benzi Palle Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel George Yin Ping Zhang
SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians.
More information about this series at http://www.springer.com/series/10030
Steven T. Dougherty
Algebraic Coding Theory Over Finite Commutative Rings
123
Steven T. Dougherty Department of Mathematics University of Scranton Scranton, PA USA
ISSN 2191-8198 SpringerBriefs in Mathematics ISBN 978-3-319-59805-5 DOI 10.1007/978-3-319-59806-2
ISSN 2191-8201
(electronic)
ISBN 978-3-319-59806-2
(eBook)
Library of Congress Control Number: 2017943819 Mathematics Subject Classification (2010): 11T71, 94B05 © The Author(s) 2017 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
For Kelly, Steve and Checco.
Acknowledgements
The author is grateful to Jessica Hollister, Meg Hudock, Josep Rifà and Mercè Villanueva for their helpful comments on an early version of the text.
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . 1.1 History . . . . . . . . . . . . . . . . . 1.2 Definitions and Notations . . . References . . . . . . . . . . . . . . . . . . .
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