Deterministic Secure Error-Correcting (SEC) Network Codes

In this paper, we propose a deterministic algorithm to construct secure error-correcting (SEC) network codes which can transmit information at rate m - 2d - k to all sink nodes, and prevent the information from eavesdropping and contamination during the transmission, where m is the minimum among the maxflows of all the sinks, d is the maximum network Hamming weight of the error vectors and k is the maximum cardinality of the subset of channels which can be eavesdropped. Such constructed network codes can also achieve the refined Singleton bound. Based on this algorithm we further present two transmission schemes which can achieve the transmission rate m - d, when the adversary satisfies an inaction assumption. We also show that in the presence of feedback, a rate beyond m - d could be possibly achieved without reconstructing the existing network code.