  In network coding, we discuss the effect of sequential error injection on
information leakage. We show that there is no improvement when the operations
in the network are linear operations. However, when the operations in the
network contains non-linear operations, we find a counterexample to improve
Eve's obtained information. Furthermore, we discuss the asymptotic rate in a
linear network under the secrecy and robustness conditions as well as under the
secrecy condition alone. Finally, we apply our results to network quantum key
distribution, which clarifies the type of network that enables us to realize
secure long distance communication via short distance quantum key distribution.
