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 (C
₁
, C
₂
) is applied at the source node, the RNGHW of the nested code (C
₂

^¿
, C
₁

^¿
) characterizes the equivocation of the wiretapper about the secure message, where C
₂
is a subcode of linear code C
₁
, and C
₁

^¿
(C
₂

^¿
) is the dual code of C
₁
(C
₂
).