Algebraic Structure Theory of Tail-Biting Trellises

It is well known that there is an intimate connection between algebraic descriptions of linear block codes in the form of generator or parity-check matrices, and combinatorial descriptions in the form of trellises. A conventional trellis for a linear code

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Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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Serdar Bozta¸s Hsiao-Feng (Francis) Lu (Eds.)

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 17th International Symposium, AAECC-17 Bangalore, India, December 16-20, 2007 Proceedings

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Volume Editors Serdar Bozta¸s RMIT University, School of Mathematical and Geospatial Sciences GPO Box 2476V, Melbourne 3001, Australia E-mail: [email protected] Hsiao-Feng (Francis) Lu National Chung-Cheng University, Department of Communications Engineering 168 University Rd., Min-Hsiung, Chia-Yi, Taiwan E-mail: [email protected]

Library of Congress Control Number: 2007940905 CR Subject Classification (1998): E.4, I.1, E.3, G.2, F.2 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13

0302-9743 3-540-77223-5 Springer Berlin Heidelberg New York 978-3-540-77223-1 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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 to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12202058 06/3180 543210

Preface

The AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard and P. Camion, organized the first conference. Originally the acronym AAECC meant “Applied Algebra and Error-Correcting Codes.” Over the years its meaning has shifted to “Applied Algebra, Algebraic Algorithms and Error-Correcting Codes,” reflecting the growing importance of complexity, particularly for decoding algorithms. During the AAECC-12 symposium the confe