GHWs of codes derived from the incidence matrices of some graphs

By the rth generalized Hamming weight of a linear code C, denoted by dr(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ d_{r}(C) $$\end{document}, we mean the smallest support size of any r-dimensional subcode of C. In this paper, we determine the rth generalized Hamming weight of the binary linear code C(G) with the parity check matrix A(G) , where the underlying graph G is a complete graph, a complete bipartite graph, a triangular graph or the Kneser graph K(n, 2) , and A(G) is the incidence matrix of G. We also obtain the rth generalized Hamming weight of the dual code of C(G) .