[IEEE Trans. on Information Theory, October 2004, pp. 2243-2256]
Linearity and Solvability in Multicast Networks
Randall Dougherty, Chris Freiling, and Kenneth Zeger
Abstract
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.