Title :
New Lower Bounds on the Generalized Hamming Weights of AG Codes
Author :
Bras-AmoroÌs, Maria ; Kwankyu Lee ; Vico-Oton, Albert
Author_Institution :
Dept. of Comput. Eng. & Math., Univ. Rovira i Virgili, Tarragona, Spain
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 :
Hamming codes; Hermitian matrices; algebraic codes; geometric codes; AG codes; Feng-Rao numbers; Garcia-Stichtenoth towers; Hermitian codes; algebraic-geometry codes; generalized Hamming weights; Conductors; Erbium; Hamming weight; Linear codes; Poles and towers; Upper bound; AG code; Feng-Rao number; Garcia-Stichtenoth towers; Hermitian codes; Numerical semigroup; generalized Hamming weights; ideal of a semigroup; isometry-dual sets of AG codes; order bound;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2014.2343993
