Scalar Linear Solvability of Matroidal Error Correction Network

Hang ZHOU  Xubo ZHAO  Xiaoyuan YANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.8   pp.1737-1743
Publication Date: 2013/08/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1737
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
network error correction code,  error pattern,  imaginary error channels,  extended network,  matroid,  

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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.