TY - JOUR
T1 - Generalized Hamming weights and some parameterized codes
AU - González Sarabia, Manuel
AU - Rentería Márquez, Carlos
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2016/2/6
Y1 - 2016/2/6
N2 - In this paper we find the complete weight hierarchy of the codes parameterized by the edges of the cycle C4 and an upper bound in the case of the complete bipartite graph K2,n. Moreover we find some bounds for the generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. These bounds work in the case of codes parameterized by the edges of any simple graph G. Also we establish the relationships among the generalized Hamming weights of any parameterized code of the form CX(d) and the generalized Hamming weights of the parameterized code of the form CX′(d), when X′ is embedded in X.
AB - In this paper we find the complete weight hierarchy of the codes parameterized by the edges of the cycle C4 and an upper bound in the case of the complete bipartite graph K2,n. Moreover we find some bounds for the generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. These bounds work in the case of codes parameterized by the edges of any simple graph G. Also we establish the relationships among the generalized Hamming weights of any parameterized code of the form CX(d) and the generalized Hamming weights of the parameterized code of the form CX′(d), when X′ is embedded in X.
KW - Embedded set
KW - Generalized Hamming weight
KW - Minimum distance
KW - Parameterized code
KW - Toric set
UR - http://www.scopus.com/inward/record.url?scp=84946607246&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2015.10.026
DO - 10.1016/j.disc.2015.10.026
M3 - Artículo
AN - SCOPUS:84946607246
SN - 0012-365X
VL - 339
SP - 813
EP - 821
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 2
ER -