Lecture Notes in Computer Science

Transcription

1 Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis 228 Applied Algebra, Algorithmics and Error-Correcting Codes 2nd International Conference, AAECC-2 Toulouse, France, October 1-5, 1984 Proceedings Edited by Alain Poli Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo

2 Editorial Board D. Barstow W. Brauer P. Brinch Hansen D. Gries D. Luckham C. Moler A. Pnueli G. Seegmi311er J. Stoer N. Wirth Editor Alain Poll AAECC/LSI Lab., Universit~ P. Sabatier 118, route de Narbonne, Toulouse C~dex, France CR Subject Classifications (1985): B.4.5, G.2.0 ISBN 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 1986 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2145/

3 PREFACE The Internation~ Colloquium on Applied Algebra and Error Correcting Codes was born in Toulouse (France) in June The acts of AAECC-I ~e publ~hed in Discrete Mathematics (vol 56 n~2-3, 0ct. 85). The acts of AAECC-2 are contained in this volume. From 48 talks, we have selected 23 accepted papers, after a (time consuming) system of multiple reviews. I thank those referees who agreed to contribute to the obtained result. I also thank : Mr. A. Oisel and CII-HBull for their financial support, ~r. M. Comb~nous Scientific Director of CNRS*, for CNRS's financi~ suppo~z, Mr. A. Dargent, Director of CNES *~ Informatic Center, for allowing us the use of the compeers before and ~'ng the conference, The LSI labor~ory and University P. Sabatier for their financial support. As one knows, digitalized data are becoming increasingly important, pa~cular- ly for transfusions. For satellite transmissions, the CCS~S (Consultative Committee for D~a Space System) had proposed a coding system for international transmissions (see : fin~ report of contract AAECC/CNES n o 84/5417, 1985 (210 pages)). Also, the targ~ of RACE project is to define and realize a Broadband-IBC european n~twork with security/privacy (cryptography) and reliability ( er~or-co~ecting co- des). AAECC lab. is a participant for the definition phase (in group n 2015). As digitalized data are b~ng more and more used for images~speech~flies trans- missions, theoretical tools and practical developments are necessary {for finite al- gebr~c structures and for comple~y analyses). In parclcular, decomposition of algebras is an interesting topic because it is used for problems involved with complex/~ (see J. Heintz/J. Morgenst~nl, for const~uzc~ tive resu~ on idempotents, mult~iv~j~&~te codes (see : A. Poll, H. Imai, A. Poli/ C. Rigoni), for DFT's problems (see : T. Beth). Many other p~ticular aspects of re- CNRS Centre National de la Recherche Scientifique ~ CNES Centre Natio~ d'etudes Spatiales (18 Av. BELIN TOULOUSE C~dexl

4 iv search are dev~oped in t~is book. Cov~n~_ra ~ s (G. Cohen/N.J.A. Sloane/A.C. Lobstun, H.F. Mattson Jr., L. Huguet/M. G*~era), o~cti_o~s~a_~o~or~_~so~_cod~ (J.A. Thiong-Ly, J~L. Dornstet~er, D.A~ Leonard/C.A. Rodg~t, B. Cou~eau/J. Goulet}, ~@acti _~ a~_~ tj of_ od~ (M.C. Gennero, G.L. Feng/K.K. Tzeng), ~ol{~o_~ a~ {P.Piret, D. iugiez, O. Moreno de Ayala), ae~li dal~ bra IH.M. M611er/F. Mora, L. Beneteau/ I. Lacaze, A. Astie-Vidal/J. Chiffl~}, c r~t{~@a~h{ (P. b_m~_ (J. Calmer, J. C~lmet/~. B~gman}. " AAECC Conferences essentkally deal with Applied Algebra, J gorkthmic and Error Correcting Cod~. The future scheduled AAECC conf@ ences are : AAECC-3 (1985, Grenoble (F), Prof. J. C~m~) AAECC-4 (1986, Karlsruhe (DJ, Prof. Dr. T. Beth) AAECC-5 (1987, Barc~ona (SP), Dr. L. Huguet). AAECC-6 (1988, Pica (I], Prof. A. ~iola) AAECC-7 (1989, Toulouse (FI, Prof. A. Poli) AAECC-8 (1990, Yokohama (J), Prof. H. Imai) We hope that.aaecc Conferences, and pa~v%icularly t@~ Lecture Notes volume, will contribute to the important dev~opment of data transmissions. Finally, a thank you to participants, authors, and also to Miss S. Watson ISpring~ Verlag Computer Science Edltori~l for h~t pc~ence and very kind help. A particular thanks to the s~ies editors who have accepted t~ publkcation. May 1986 Alain POLI

5 CONTENTS J. HEINTZ, J. MORGENSTERN "On associative algebras of minimal rank" A. POLl "Construction of primitive idempotents for n variable codes" H. IMAI "Multivariate polynomials in coding theory" A. POLl, C. RIGONI "Enumeration of self dual 2k circulant codes" T. BETH "Codes, groups and invariants" G.D. COHEN, A.C. LOBSTEIN, N.J.A. SLOANE "On a conjecture concerning coverings of Hamming space" H.F. MATTSON Jr. "An improved upper bound on covering radius" L. HUGUET, M. GRIERA "Association schemes and difference sets defined on two weight codes" J.A. THIONG-LY "Automorphisms of two families of extended non binary cyclic Goppa codes" J.L. DORNSTETTER "Some quasi-perfect cyclic codes" D.A. LEONARD, C.A. RODGER "Explicit Kerdock codes over GF(2)" B. COURTEAU, J. GOULET "Une classe de codes 2-correcteurs adapt#s aux syst~mes d'information format,s" M.C. GENNERO "LOUSTICC simulation software : experimental results of coding systems" G.L. FENG, K.K. TZENG "An algorithm of complete decoding of double-error-correcting Goppa codes" P. PIRET "On the number of divisors of a polynomial over GF(2)" D. LUGIEZ "Multivariate polynomial factoring and detection of true factors" O. MORENO DE AYALA "Discriminants and the irreducibility of a class of polynomials" H.M. MOLLER, F. MORA "Computational aspects of reduction strategies to construct resolutions of monomialideals" I

6 Vi L. BENETEAU, J. LACAZE "Designs arising from symplectic geometry" A. ASTIE-VlDAL, J. CHIFFLET "Distance-transitive graphs and the problem of maximal subgroups of symmetric groups" P. CAMION "Can a fast signature scheme without secret key be secure?" J. CALMET "Manipulation of recurrence relations in computer algebra" J. CALMET, M. BERGMAN "Some design principles for a mathematical knowledge representation system : a new approach to scientific calculation"