A network coding system. A packet decoding engine receives a number of received packets. A packet repository is coupled to the decoding engine to temporarily store the received packets. The packet decoding engine is configured to generate a decoding matrix by forming a sub-matrix by selecting columns of a network code matrix that have indices that are the same as the indices of the encoded packets that correspond to the selected received packets. The packet decoding engine is also configured to invert the sub-matrix to form the decoding matrix and multiply the received packet matrix by the decoding matrix to generate a recovered matrix where each column corresponds to a decoded packet.