Abstract
We give an algorithm to factorize a polynomial F of k[X,Y], where k is a perfect field. We define a projective plane curve C associated to F and we construct basis for k-vector spaces M(D), D beeing a divisor on the smooth projective model of C. This can be done using the generalization of Brill-Noether algorithm to the non-irreducible case. We recall that, in coding theory, this algorithm constructs the generator matrices (or the check matrices) of algebraic-geometric Goppa codes associated to absolutely irreducible projective plane curves.
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© 1989 Springer-Verlag Berlin Heidelberg
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Le Brigand, D. (1989). Polynomial factorization using Brill-Noether algorithm. In: Cohen, G., Wolfmann, J. (eds) Coding Theory and Applications. Coding Theory 1988. Lecture Notes in Computer Science, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019845
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DOI: https://doi.org/10.1007/BFb0019845
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