15th AAECC Symposium
Applied Algebra, Algebraic Algorithms,
and Error Correcting Codes
Toulouse (France)
May 12-16 , 2003
Topics
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Algebra
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Complexity in all algebraic constructions
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Algebraic complexity theory
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Gröbner bases: structure, and solution of integer programs...
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bases of fields : finite fields, cyclotomic fields..., special bases, optimal
bases...
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explicit constructions : irreducible polynomials, factorizing polynomials...
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finite structures : Galois rings, codes over rings (Z_4, local and semi-local
rings, Gray maps)...
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effective algebra : Nullstellensatz, linear algebra...
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multivariate polynomial problems, factorization/decomposition of multiv.
polynomials, multivariate polynomial applications...
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Codes and Algebra
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algebraic codes : cyclic, double circulant, abelian codes...
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multiv. polynomial codes, concatenated codes, product codes...
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decoding methods and their complexity : algorithms for AG codes, Gröbner
bases and decoding, trellis decoding, Turbo decoding, iterative algorithms
for concatenated codes...
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AG-codes, algebraic Geometry over finite fields...
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automorphisms of codes...
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Codes and Combinatorics
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Hadamard and weighting matrices, highly regular graphs from cosets, designs
in codewords, r-partition designs, orthog. arrays, (t,m,s)-nets...
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euclidean lattices (spherical codes and designs, decoding, vector quantizing,
higher dimensional modulation)...
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Modulation and Codes, Sequences
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unequal error protection, coset codes, multidimensional trellis coded modulation,
multilevel coding...
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lattices : Gaussian channel modulation...
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sequences (low correlation for spread spectrum and CDMA, Hamming correlation
for FHMA, pseudo-random sequences for cryptography, complexity profile)...
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Cryptography
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public-key Cryptography, elliptic curve cryptosystems, computational number
theory, authentication and digital signatures, Hash Functions, zero-knowledge
proofs, pseudorandom numbers and sequences, stream ciphers and block ciphers...
Invited Speakers
Monday 12 - P.
Solé
(Cryptography & Algebra) : Public key cryptosystems
based on rings
Tuesday 13 - S. Lin (Codes)
:
Combinatoric Low Density Parity Check Codes
Tuesday 13 - J. Stern(Cryptography)
: Cryptography and the methodology of provable security
Thursday 15 - D. Costello(Codes)
: Graph-based convolutional LDPC codes
Thursday 15 - I. Shparlinsky(Codes
& Algebra) : Dynamical systems generated by rational functions
Friday 16 - A.
Lauder(Algebra) : Algorithms for multivariate polynomials
over finite fields