An application of the relative network Generalized Hamming weight to erroneous wiretap networks

This paper demonstrates that the relative network generalized Hamming weight (RNGHW) of a nested code fully characterizes the security performance of the corresponding nested coset coding scheme for erroneous wiretap networks with a given linear network code. Specifically, when the nested coset coding specified by a nested code (C1, C2) is applied at the source node, the RNGHW of the nested code (C2¿, C1¿) characterizes the equivocation of the wiretapper about the secure message, where C2is a subcode of linear code C1, and C1¿(C2¿) is the dual code of C1(C2).