A sharp upper bound for the maximum integer not belonging to an ideal of anumerical semigroup is given and the ideals attaining this bound arecharacterized. Then the result is used, through the so-called Feng-Rao numbers,to bound the generalized Hamming weights of algebraic-geometry codes. This isfurther developed for Hermitian codes and the codes on one of theGarcia-Stichtenoth towers, as well as for some more general families.
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