Linearity and Solvability in Multicast Networks
Randall L. Dougherty, C. Freiling, K. Zeger · IEEE Transactions on Information Theory · 2004
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.