Lecture Notes in Computer Science

Transcription

1 Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis 229 I I Algebraic Algorithms and Error-Correcting Codes 3rd International Conference, AAECC-3 Grenoble, France, July 15-19, 1985 Proceedings Edited by Jacques Calmet Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo

2 Editorial Board D. Barstow W. Brauer R Brinch Hansen D. Gries D. Luckham C. Moler A. Pnueli G. SeegrnLitler J. Stoer N. Wirth Editor Jacques Calmet LIFIA, BP Saint Martin d'h~res C~dex, France CR Subject Classifications (1985): E.4, 1.1 ISBN "76-5 Springer-Verlag Berlin Heidelberg New York ISBN Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich, Springer-Verlag Berlin Heidelberg 1985 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2145/

3 PREFACE The AAECC conferences began in Toulouse in The proceedings of AAECC-1 were published as a special issue of Discrete Mathematics. The proceedings of AAECC-2 are also published by Springer-Verlag as a volume in the Lecture Notes in Computer Science series. This third conference was organized by the "Laboratoire d'informatique Fondamentale et d'intelligence Artificielle" (LIFIA) in Grenoble on July 15-19, It was held in the building of the "Ecole Nationale Sup~rieure d'ing~nieurs en Informatique et Math~matiques Appliqu~es" of the National Polytechnic Institute of Grenoble. The main motivation for this series of conferences was to gather researchers in error-correcting codes, applied algebra and algebraic algorithms. The latter topic has been extended to computer algebra in general. Applied algebra must be understood as applied to computer science. After three conferences, it appears that they fill a communication gap. It is thus natural that the AAECC conferences are going to be held annually in different countries. For this reason, a permanent organizing committee has been set up. It consists of: Thomas Beth, Jacques Calmet, Anthony C. Hearn, Joos Heintz, Hideki Imai, Heinz Liineburg, H.F. Mattson Jr. and Alain Poll The next conferences will be held in Karlsruhe (1986), Barcelona (1987), Pisa or Roma (1988), Toulouse (1989) aud Yokohama (1990). I am very grateful to the following institutions and organizations for their generous funding of the conference:. DRET (Direction des Recherches, Etudes et Techniques du Minist~re de la D~fense) CNRS (Centre National de la Recherche Scientifique) SMF (Soci~t~ Math~matique de France) INPG (Iustitut National Polytechnique de Grenoble) Mairie de Grenoble Conseil G~n~ral de l'is~re. No conference is successful without many people contributing their time and efforts in its preparation. The referees did an excellent job in reading and evaluating many papers in a very short amount of time, both before and after the meeting was held. The session chairpersons were very efficient in keeping the conference on tracks. A special thanks is deserved by Alain Poll who made available to me his experience of organizing the previous AAECC conferences. The local organization ran smoothly because of the help of Ph. Chatelin. Isabelle Michel has been a very efficient and pleasant conference secretary. G. Veillon, the ENSIMAG director, provided us with all the help we required. I extend my warmest thanks to all of them. Jacques Calmet May 1986

4 ORGANIZING COMMITTEE Th. BETH, University of London, England and University of Karlsruhe, FRG J. CALMET, LIFIA, Grenoble, France (Conference Chairman) A.C. HEARN, The Rand Corporation, Santa Monica, USA H. LUNEBURG, University of Kaiserslautern, FRG A. POLI, University Paul Sabatier, Toulouse, France SCIENTIFIC COMMITTEE B. BUCHBERGER, University J. Kepler, Linz, Austria P. CAMION, INRIA, Rocqueneourt, France B.F. CAVINESS, University of Delaware, Newark, USA G.E. COLLINS, University of Wisconsin at Madison, USA B. COURTEAU, Sherbrooke University, Canada J.H. DAVENPORT, University of Bath, England E. ENGELER, ETH, ZSrich, Switzerland J. HEINTZ, Univ. Frankfurt and IAM, Buenos Aires, Argentina L. HUGUET, Autonomous University of Barcelona, Spain H. IMAI, Yokohama National University, Japan D. LAZARD, University of Paris VI, France R. LOOS, University of Karlsruhe, FRG H.F. MATTSON Jr., Syracuse University, USA A. MIOLA, IASI-CNR, Roma, Italy Ph. PIRET, Philips Research Lab., Brussels, Belgium C.C. SIMS, Rutgers University, New Brunswick, USA H. ZASSENHAUS, Ohio State University, Colombus, USA LOCAL ORGANIZATION: J. CALMET and Ph. CHATELIN, LIFIA, Grenoble, France List of Referees J.A. Abbott, Th. Beth, B. Buchberger, R. Caferra, J. Calmet, P. Camion, B.F. Caviness, G. Cohen, G.E. Collins, B. Courteau, J.H. Davenport, K. Dittenberger, E. Engeler, R. Gebauer, K.O. Geddes, A.C. Hearn, J. Heintz, L. Huguet, H. Imai, D. Lazard, A. Leitsch, R. Loos, H. Liineburg, H.F. Mattson Jr., A. Miola, F. Mora, J. Padget, Ph. Piret, A. Poll, C.C. Sims, J. Smit, F. Winkler, H. Zassenhaus. Session chairpersons M. Bergman, B.Buchberger, P. Camion, B. Courteau, K.O. Geddes, C. Goutelard, A.C. Hearn, J. Heintz, L. Huguet, H. Imai, H. LSneburg, T. Matsumoto, H.F. Mattson Jr., A. Miola, F. Mora, M.F. Newman, A. Poll, V. Weispfenning, J. Wolfmann.

5 TABLE OF CONTENTS Introduction... 1 On the Arithmetics of Galois fields and The Like... 2 (Algebraic Questions Arising in the Design of Secure Communication Systems) Th. Beth (University of Karlsruhe) (Invited) On Strongly Tactical Codes M. Gundlaeh (University of Mainz) Integer Programming Applied to gigenvector Computation in a Class of Markov Processes A. Oisel (CII-Honeywell Bull Co.) A Minimum System of Generators for Extended Cyclic Codes which are Invariant under the Affine Group P. Charpin (University of Paris VI) Some Algebraic Tools for Error-Correcting Codes A. Poll (University P. Sabatier of Toulouse) (Invited) On Computing the Performance Probabilities of Reed-Solomon Codes S. Jennings (Racal Research Ltd. Reading) Numerical Experiments Related to the Covering Radius of Some First Order Reed-Muller Codes J. Constantln, B. Courteau (University of Sherbrooke) J. Wolfmann (University of Toulon) Several Aspects of Problems Encountered in Coding Applications C. Goutelard (LETTI, Paris) (Invited) Software Simulation of Data Transmission Using Error-Correcting Codes Through an A WGN Channel M.C. Gennero and D. ttandriananja (University P. Sabatier of Toulouse) Algebraic Methods for Constructing Asymmetric Cryptosystems H. Imai (Yokohama National University) (Invited) T. Matsumoto (University of Tokyo) Covering Radii of Even Subcodes of t-dense Codes H. Janwa and H.F. Mattson, Jr. (Syracuse University, NY) (Invited) Orthogonal Transform Encoding of Cyclic Codes W. Fumy (University of Erlangen-Nuremberg) On S-Sum-Sets and Projective Codes M. Grlera, J. Rif~ and L. Huguet (Autonomous University Barcelona) Pseudo-Triple-Sum-Sets and Association Schemes L. Huguet, J. Rif~ and M. Grlera (Autonomous University Barcelona) A Decoding Algorithm for Linear Codes M. Bossert and F. Hergert (TH Darmstadt) The Finite Fourier-Transform and Theta Functions H. Opolka (University of GSttingen)

6 Yl Recent Results on Coding and Algebraic Geometry J. Wolfmann (University of Toulon) (Invited) Some Properties of Elliptic Codes Over a Field of Characteristic ~ Y. Driencourt (University of Paris 7) Self-Dual Codes tn Circulant Over Fq (q = 2") A. Poli and C. Rigoni (University P. Sabatier of Toulouse) Automorphisms and Isometrics of Some Modular Algebras M. Ventou (University P. Sabatier of Toulouse) A Lower Bound for the Bilinear Complexity of Some Semisimple Lie Algebras H.F. de Groote (J.W. Goethe University of Frankfurt) J. Heintz (I A M, Buenos Aires) (Invited) On Computational Complexity of Some Algebraic Curves Over Finite Fields D. Le Brigand (University of Paris VI) Some Group Presentations and Enforcing the Associative Law M.F. Newman (Australian National University) (Invited) Fast Computation of Linear Finite-Dimensional Operators over Arbitrary Rings E.G. Belaga (University L. Pasteur Strasbourg) Quantifier Elimination for Real Closed Fields W. Bfge (University of Heidelberg) (Invited) Efficient Decision Algorithms for Locally Finite Theories V. Weispfenning (University of Heidelberg) The Algorithmic Structure of sl(2, k) R. Mirwald (J.W. Goethe University of Frankfurt) Optimal Algorithms for Finite Dimensional Simply Generated Algebras A. Fellmann (J.W. Goethe University of Frankfurt) On a Little but Useful Algorithm H. Liineburg (University of Kaiserslautern) (Invited) Computation of Independent Units in Number Fields by Diriehlet's Method J. Buchmann (University of KSln) A. Peth5 (Kossuth Lajos Univ. Debrecen) Some Upper Bounds for the Multiplicity of an Autoredueed Subset of N '~ and their Applications G. Carr~ Ferro (University of Catania) Exact Computation of the Characteristic Polynomial of an Integer Matrix A. Mukhopadhyay and V.S. Alagar (Concordia University Montreal) An Analysis of the Kr6necker Algorithm for Factorization of Algebraic Polynomials R. Logs (University of Karlsruhe) (Invited) Polynomial Faetorization over Z[z] G. Viry (CRIN Nan~y) The L.Mashine: An Attempt at Parallel Hardware for Symbolic Computation B. Buchberger (J. Kepler University Linz) (Invited) An Interactive Graphical Interface for Symbolic Algebra Systems Wm Leler and N. Soiffer (Tektronix Inc.)

7 VII Gra,.bner Bases for Non-Commutative Polynomial Rings F. Mora (University of Genova) Eztending the Binary GCD Algorithm... : G.H. Norton (University of Bristol) Integration of Rational Functions in SA G-~ T.J. Smedley (Univ. of Karlsruhe and Univ. of Waterloo) tieuristle Bivarlate Lifting D. Lugiez (Univ. Karlsruhe and LIFIA Grenoble) Optimal Evaluation of Algebraic Ezpressions A.C. Hearn (The Rand Corporation) (Invited) On Deleting Links in Semantic Graphs N.V. Murray and E. Rosenthal (State Univ. of N.Y. at Albany) Author Index