Workshop Report: Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes

H. F. Mattson

The international symposium AAECC 11 was held in Paris last summer, from July 16 to July 20. All lectures took place in the ``old" Ecole Polytechnique, just down the hill from the Pantheon.

These symposia cover topics that share the use of algebraic methods and techniques for applications in computing, communications, and engineering. So far the preponderance of papers at these symposia have been in computer algebra and error-correcting codes. Readers of this Newsletter know the latter subject, but computer algebra, on the other hand, may be foreign territory to some. Computer algebra is devoted to the investigation of algorithms, computational methods, software systems, and computer languages oriented to scientific computations performed on exact and often symbolic data, by manipulating formal expressions according to the algebraic rules they satisfy.

Some threads in coding that are especially relevant to computer algebra are algebraic-geometric codes and the use of Groebner bases to devise decoding algorithms. AAECC was the first symposium with papers in the latter specialty (AAECC 2, 1984 (Imai); AAECC 3, 1985 (Poli); AAECC 7, 1989, & AAECC 9, 1991 (Sakata)). All along AAECC has had many papers on Groebner bases in ``pure" computer algebra.

``AAECC" has come to stand for ``Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes." The Proceedings, refereed to the same standards as journals, were handed to participants at registration. The current Proceedings are published by Springer as no. 948 in Lecture Notes in Computer Science (LNCS). Editors were G. Cohen, M. Giusti, and T. Mora, who also organized the symposium. The list of speakers, with titles of the papers they presented at AAECC 11, is below.

The twelfth AAECC will be held in Toulouse, France, in July 1997. We hope to increase the proportion of papers in applied coding at AAECC 12. The preliminary Call for Papers will appear in a future issue of the Newsletter.

Contrary to the usual practice at AAECC, there was no excursion organized for AAECC 11 owing to the lack of places to go and things to do in the environs of the Symposium. There was a banquet, however, held on a beautiful summer evening in the restaurant of the Eiffel Tower.

List of Talks at AAECC 11

Invited talks
L. A. Bassalygo:
Supports of a Code.
I. Honkala:
On Algebraic Methods in Covering Radius Problems.
A. Kerber:
Chemical Isomerism, a Challenge for Algebraic Combinatorics and for Computer Science.
L. M. Pardo:
How Lower and Upper Complexity Bounds Meet in Elimination Theory.
A. Schoenhage:
Bivariate Polynomial Multiplication Patterns.

Contributed talks
J. Apel:
Division of Entire Functions by Polynomial Ideals.
I. Armendariz, P. Solerno:
On the Computation of the Radical of Polynomial Complete Intersection Ideals.
A. Ashikhmin, A. Barg, G. Cohen, L. Huguet:
Variations on Minimal Codewords in Linear Codes.
V. B. Balakirsky:
On Interval Linear Complexity of Binary Sequences.
T. Beth, H. Kalouti, D. E. Lazic:
Which Families of Long Binary Linear Codes Have a Binomial Weight Distribution?
A. Betten, A. Kerber, A. Kohnert, R. Laue, A. Wassermann:
The Discovery of Simple 7-Designs with Automorphism Group .
I. Bocharova, B. D. Kudryashov:
Fast Exponentation in Cryptography.
G. Carrà-Ferro:
A Resultant Theory for the Systems of Two Ordinary Algebraic Homogeneous Differential Equations
A. Colin:
Formal Computation of Galois Groups with Relative Resolvent Polynomials.
P. Conti, C. Traverso:
A Case of Automatic Theorem Proving in Euclidean Geometry: the Maclane Theorem.
G. Cooperman, L. Finkelstein:
Cayley Graph Techniques for Permutation Routing on Bus Interconnection Networks .
H. Fripertinger, A. Kerber:
Isometry Classes of Indecomposable Linear Codes.
M. Giusti, J. Heintz, J. E. Morais, L. M. Pardo:
When Polynomial equation Systems Can Be ``Solved'' Fast?
L. González-Vega, G. Trujillo:
Using Symmetric Functions to Describe the Solution Set of a Zero-Dimensional Ideal.
H. G. Graebe:
Triangular Systems and Factorized Groebner Bases.
G. Haché:
Algebraic-Geometric Codes.
H. Hong:
Implicitization of Curves Parameterized by Generalized Trigonometric Polynomials.
J. Iwatani, H. Imai:
Code Construction for Frequency Hopping Multiple Access Communication Systems.

Y. Kamiya, T. Miki, Y. Iwadare:
Randomness Properties of Partial - Planes. P.-V. Koseleff:
About Approximations of Exponentials.
J. Lacan, E. Delpeyroux:
A Note on Normal Bases.
F. Levy-dit-Vehel, S. Litsyn:
On the Covering Radius of Long Goppa Codes.
G. Matera:
Integration of Multivariate Rational Functions Given by Straight-line Programs.
M. Moreno Maza, R. Rioboo:
Polynomial Gcd Computations over Towers of Algebraic Extensions.
Q. L. Nguyen, D. H. Wood:
Displacements of Matrix Products.
A. Péladan-Germa:
Testing Identities of Series Defined by Algebraic Partial Differential Equations.
J. F. Ragot:
A Method of Absolute Factorization of Polynomials in Two Variables over Q. Improvement and Implementation.
F. Rebufat:
Somme de Minkowski de Deux Polygones Courbes Convexes en Rotation.
F. Rouillier, M.-F. Roy, A. Szpirglas:
Multivariate Symmetric Functions and Polynomial System Solving.
B. Sadik:
The Complexity of Formal Resolution of Linear Partial Differential Equations.
S. Sakata, M. Kurihara:
A Fast Parallel Implementation of the Berlekamp-Massey. Algorithm with a One-D Systolic Array Architecture.
P. Schapira:
Tomography of Constructible Functions.
J. A. Shih:
On the Determination of Formal Solution of a System of Partial Differential Equations.
P. Solé:
D , E , E and the AGM.
A. Valibouze:
Computation of the Galois Groups of the Resolvant Factors
for the Direct and Inverse Galois Problem.
P. Veron:
An Identification Scheme Based on Trace Operator.
J. A. Weil:
First Integrals and Darboux Polynomials of Homogeneous Linear Differential Systems.

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