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Homepage: http://www.irit.fr/ACTIVITES/AAECC/A13.shtm
Organizers: Shu Lin, A. Poli
Description:
Topics
Algebra Complexity in all algebraic constructions Groebner bases: structure, and solution of integer programs... bases of fields : finite fields, cyclotomic fields..., special bases, optimal bases... explicit constructions : irreducible polynomials, factorizing polynomials... finite structures : Galois rings, codes over rings (Z_4, local and semi-local rings, Gray maps)... effective algebra : Nullstellensatz, linear algebra... multivariate polynomial problems, factorization/decomposition of multiv. polynomials, multivariate polynomial applications...
Codes and Algebra algebraic codes : cyclic, double circulant, abelian codes... multiv. polynomial codes, concatenated codes, product codes... decoding methods and their complexity : algorithms for AG codes, Groebner bases and decoding, trellis decoding, Turbo decoding, iterative algorithms for concatenated codes... AG-codes, algebraic Geometry over finite fields... automorphisms of codes...
Codes and Combinatorics Hadamard and weighting matrices, highly regular graphs from cosets, designs in codewords, r-partition designs, orthog. arrays, (t,m,s)-nets... euclidean lattices (spherical codes and designs, decoding, vector quantizing, higher dimensional modulation)...
Modulation and Codes, Sequences unequal error protection, coset codes, multidimensional trellis coded modulation, multilevel coding... lattices : Gaussian channel modulation... sequences (low correlation for spread spectrum and CDMA, Hamming correlation for FHMA, pseudo-random sequences for cryptography, complexity profile)...
Cryptography public-key Cryptography, elliptic curve cryptosystems, authentication and digital signatures, Hash Functions, zero-knowledge proofs, pseudorandom numbers and sequences, stream ciphers and block ciphers...
Speakers: I.F. Blake, M. Clausen, G.D. Forney Jr., R.J. McElice, B. Sturmfels
Date received: February 22, 1999
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