Polynomial time algorithms for multicast network code construction

By Sidharth Jaggi, Peter Sanders, P. Chou, Michelle Effros, S. Egner, Kamal Kumar Jain, L. Tolhuizen. IEEE Transactions on Information Theory, 2005

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Network coding for efficient communication in extreme networks (2005, background): “When a node receives m combinations of n packets, it can decode them provided that the set of combinations has rank n; for m = n this occurs with a probability close to 1 if the coefficients gi are chosen randomly and independently at every node[10].”
Resilient Network Coding in the Presence of Byzantine Adversaries (2008, positive): “The combination of [23], [21], and [15] shows that, for multicast traffic, linear codes achieve the maximum capacity bounds, and both design and implementation can be done in polynomial time.”
Minimum-cost multicast over coded packet networks (2005, background): “, [2], [3], [4], [5], [6], have built upon their work.”
The Importance of Being Opportunistic: Practical Network Coding for Wireless Environments (2005, background): “variety of coding and decoding options [8, 13–16, 19–21], network coding has established its theoretical ability to improve network throughput.”