Generalized Hamming weights and some parameterized codes

In this paper we find the complete weight hierarchy of the codes parameterized by the edges of the cycle C4C4 and an upper bound in the case of the complete bipartite graph K2,nK2,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 GG. Also we establish the relationships among the generalized Hamming weights of any parameterized code of the form CX(d)CX(d) and the generalized Hamming weights of the parameterized code of the form CX′(d)CX′(d), when X′X′ is embedded in XX.