New Lower Bounds on the Generalized Hamming Weights of AG Codes

Maria Bras-Amorós, Kwankyu Lee, Albert Vico-Oton

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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