Scalar Linear Solvability of Matroidal Error Correction Network
In this paper, we further study linear network error correction code on a multicast network and attempt to establish a connection between linear network error correction codes and representable matroids. We propose a similar but more accurate definition of matroidal error correction network which has been introduced by K. Prasad et al. Moreover, we extend this concept to a more general situation when the given linear network error correction codes have different error correcting capacity at different sinks. More importantly, using a different method, we show that a multicast error correction network is scalar-linearly solvable if and only if it is a matroidal error correction network.
matroid network error correction code error pattern imaginary error channels extended network