Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Lower Bounds on the Generalized Hamming Weights of AG Codes   A sharp upper bound for the maximum integer not belonging to an ideal of a
numerical semigroup is given and the ideals attaining this bound are
characterized. Then the result is used, through the so-called Feng-Rao numbers,
to bound the generalized Hamming weights of algebraic-geometry codes. This is
further developed for Hermitian codes and the codes on one of the
Garcia-Stichtenoth towers, as well as for some more general families.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: funct-an