New Lower Bounds on the Generalized Hamming Weights of AG Codes
Information Theory
2017-06-30 v1 math.IT
Abstract
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.
Keywords
Cite
@article{arxiv.1706.09770,
title = {New Lower Bounds on the Generalized Hamming Weights of AG Codes},
author = {Maria Bras-Amorós and Kwankyu Lee and Albert Vico-Oton},
journal= {arXiv preprint arXiv:1706.09770},
year = {2017}
}