Algebraic Algorithms and Error-Correcting Codes -

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Résumé :
On the arithmetics of Galoisfields and the like.- On strongly tactical codes.- Integer programming applied to eigenvector computation in a class of Markov processes.- A minimum system of generators for extended cyclic codes which are invariant under the affine group.- Some algebraic tools for error-correcting codes.- On computing the performance probabilities of Reed-Solomon codes.- Numerical experiments related to the covering radius of some first order Reed-Muller codes.- Several aspects of problems encountered in coding applications.- Software simulation of data transmission using error-correcting codes, through an awgn channel.- Algebraic methods for constructing asymmetric cryptosystems.- Covering radii of even subcodes of t-dense codes.- Orthogonal transform encoding of cyclic codes.- On s-sum-sets and projective codes.- Pseudo-triple-sum-sets and association schemes.- A decoding algorithm for linear codes.- The finite Fourier-transform and theta functions.- Recent results on coding and algebraic geometry.- Some properties of elliptic codes over a field of characteristic 2.- Self-dual codes 2n circulant over Fq (q=2r).- Automorphisms and isometries of some modular algebras.- A lower bound for the bilinear complexity of some semisimple lie algebras.- On computational complexity of some algebraic curves over finite fields.- Some group presentations and enforcing the associative law.- Fast computation of linear finite-dimensional operators over arbitrary rings.- Quantifier elimination for real closed fields.- Efficient decision algorithms for locally finite theories.- The algorithmic structure of dollars dollars\mathfrak{s}\mathfrak{l}(2,k) dollars dollars .- Optimal algorithms for finite dimensional simply generated algebras.- On a little but useful algorithm.- Computation of independent units in number fields by Dirichlet's method.- Some upper bounds for the multiplicity of an autoreduced subset of N m and their applications.- Exact computation of the characteristic polynomial of an integer matrix.- An analysis of the Kr?necker algorithm for factorization of algebraic polynomials.- Polynomial factorization over ?[X].- The L-machine: An attempt at parallel hardware for symbolic computation.- An interactive graphical interface for symbolic algebra systems.- Groebner bases for non-commutative polynomial rings.- Extending the binary GCD algorithm.- Integration of rational functions in SAC-2.- Heuristic bivariate lifting.- Optimal evaluation of algebraic expressions.- On deleting links in semantic graphs.- Erratum.

Sommaire:
On the arithmetics of Galoisfields and the like.- On strongly tactical codes.- Integer programming applied to eigenvector computation in a class of Markov processes.- A minimum system of generators for extended cyclic codes which are invariant under the affine group.- Some algebraic tools for error-correcting codes.- On computing the performance probabilities of Reed-Solomon codes.- Numerical experiments related to the covering radius of some first order Reed-Muller codes.- Several aspects of problems encountered in coding applications.- Software simulation of data transmission using error-correcting codes, through an awgn channel.- Algebraic methods for constructing asymmetric cryptosystems.- Covering radii of even subcodes of t-dense codes.- Orthogonal transform encoding of cyclic codes.- On s-sum-sets and projective codes.- Pseudo-triple-sum-sets and association schemes.- A decoding algorithm for linear codes.- The finite Fourier-transform and theta functions.- Recent results on coding and algebraic geometry.- Some properties of elliptic codes over a field of characteristic 2.- Self-dual codes 2n circulant over Fq (q=2r).- Automorphisms and isometries of some modular algebras.- A lower bound for the bilinear complexity of some semisimple lie algebras.- On computational complexity of some algebraic curves over finite fields.- Some group presentations and enforcing the associative law.- Fast computation of linear finite-dimensional operators over arbitrary rings.- Quantifier elimination for real closed fields.- Efficient decision algorithms for locally finite theories.- The algorithmic structure of $$\mathfrak{s}\mathfrak{l}(2,k)$$ .- Optimal algorithms for finite dimensional simply generated algebras.- On a little but useful algorithm.- Computation of independentunits in number fields by Dirichlet's method.- Some upper bounds for the multiplicity of an autoreduced subset of N m and their applications.- Exact computation of the characteristic polynomial of an integer matrix.- An analysis of the Kr?necker algorithm for factorization of algebraic polynomials.- Polynomial factorization over ?[X].- The L-machine: An attempt at parallel hardware for symbolic computation.- An interactive graphical interface for symbolic algebra systems.- Groebner bases for non-commutative polynomial rings.- Extending the binary GCD algorithm.- Integration of rational functions in SAC-2.- Heuristic bivariate lifting.- Optimal evaluation of algebraic expressions.- On deleting links in semantic graphs.- Erratum....