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 C₂ is a subcode of linear code C₁, and C₁ ^¿ (C₂ ^¿) is the dual code of C₁ (C₂).