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Algebraic geometry codes from order domains

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Gröbner Bases, Coding, and Cryptography Massimiliano Sala · Teo Mora · Ludovic Perret · Shojiro Sakata · Carlo Traverso Editors Gröbner Bases, Coding, and Cryptography Massimiliano Sala University College Cork Boole Centre for Research in Informatics Crosses Green 17 South Bank Cork, Ireland [email protected] Teo Mora Università Genova Dipto. Matematica Via Dodecaneso, 35 16146 Genova, Italy [email protected] Ludovic Perret University of Paris VI, LIP6 104 avenue du Président Kennedy 75016 Paris, France [email protected] Shojiro Sakata Toyohashi University of Technology Faculty of Engineering Dept. Production Systems Engineering 1-1 Hibarigaoka Toyohashi, Aichi Tempaku-cho 441-8580, Japan [email protected] Carlo Traverso Università Pisa Dipto. Matematica Largo Bruno Pontecorvo, 5 56127 Pisa, Italy [email protected] ISBN 978-3-540-93805-7 DOI 10.1007/978-3-540-93806-4 e-ISBN 978-3-540-93806-4 Library of Congress Control Number: 2008944307 © 2009 Springer-Verlag Berlin Heidelberg 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 to prosecution under the German Copyright Law. 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. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 Preface Massimiliano Sala In the period February–July 20

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