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Nullity(X) = dim(Π ⊥ X ). 2 J. Wang et al. Network Model This paper concentrates on the multicast communication. The source node is responsible for the distribution of data packets and the providing of detection information. Intermediate nodes are responsible for the verification of received packets and the transmission of data packets. Sink node belongs to a special kind of intermediate node. In addition to have the operations of intermediate nodes, sink nodes still have decoding operations to recover the original data source node transmitted.

Theory 54(8), 3579–3591 (2008) 23. : SNKC: an efficient on-the-fly pollution detection scheme for content distribution with linear network coding. In: Proceedings of International Conference on Embedded and Ubiquitous Computing, pp. 2298–2305 (2013) Short Null Keys Based Secure Network Coding Against Pollution Attacks 31 24. : On-the-fly verification of rateless erasure codes for efficient content distribution. In: Proceedings of IEEE Symposium on Security and Privacy, pp. 226–240 (2004) 25. : The probability distribution of the matrix rank on fq and the asymptotic properties of the rank.

Rack r1 and r2 are put in the any place of a data center, and servers on the top storey can connect with each other by reflecting the wireless signal to the mirror. Without loss of generality, we can set up the connection between r1 and r2 by adjusting the directional antennas to set up a wireless link. This design has two advantages at least. First, if the data center is deployed and the position of a rack is fixed, we can set up the wireless link between any two racks by adjusting the directional antennas.

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