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Recently, XOR-based network coding has been demonstrated as an effective approach to improve the network performance for wireless broadcast. In this way, the source XOR multiple lost packets from different receivers into one packet and retransmits it, then multiple receivers are able to recover their lost packets, which can effectively reduce the number of retransmissions and utilize wireless bandwidth. However, to find the optimal XOR coding set that minimizes the total number of transmissions has been proved as NP-hard and of high complexity. In this paper, we proposed a new wireless broadcast retransmission scheme based on linear random network coding, in which the source code combines all lost packets to a single one by linear network coding for retransmission, and receivers are able to decode the original packets by method of Gaussian elimination when they receive enough coded-packets. Simulation results are given to demonstrate superior performance of our algorithm over previously proposed works.