Linearity and solvability in multicast networks

@article{Dougherty2004LinearityAS,
  title={Linearity and solvability in multicast networks},
  author={Randall Dougherty and Christopher F. Freiling and Kenneth Zeger},
  journal={IEEE Transactions on Information Theory},
  year={2004},
  volume={50},
  pages={2243-2256}
}
It is known that for every solvable multicast network, there exists a large enough finite-field alphabet such that a scalar linear solution exists. We prove: i) every binary solvable multicast network with at most two messages has a binary scalar linear solution; ii) for more than two messages, not every binary solvable multicast network has a binary scalar linear solution; iii) a multicast network that has a solution for a given alphabet might not have a solution for all larger alphabets. 
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