Linear Network Coding, Linear Index Coding and Representable Discrete Polymatroids

@article{Muralidharan2016LinearNC,
  title={Linear Network Coding, Linear Index Coding and Representable Discrete Polymatroids},
  author={Vijayvaradharaj T. Muralidharan and B. Sundar Rajan},
  journal={IEEE Transactions on Information Theory},
  year={2016},
  volume={62},
  pages={4096-4119}
}
Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding, and representable discrete polymatroids. We consider the vector linear solutions of networks over a field Fq, with possibly different message and edge vector dimensions, which are referred to as linear fractional solutions. It is well known that a scalar linear solution over Fq exists for a network if and only if the network is matroidal with… CONTINUE READING
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