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Wireless network coding (WNC) has been considered as a promising solution with its capability of improving the overall performance of wireless mesh networks. A problem caused when WNC is employed in multi-rate wireless networks is that the link status between the relay node and intended receivers of a coded packet is mutually different. Even though there are links that support higher transmission rates, the relay node must transmit the coded packet at the lowest transmission rate among intended links' rates for the successful reception at all intended receivers. In this paper, we propose a WNC scheme that is combined with Forward Error Correction (FEC) to alleviate the problem explained above. The proposed scheme tries to transmit coded packets with a transmission rate higher than the lowest transmission rate so that the time required to transmit coded packets is reduced. However, it may increase the error rate. To compensate for the increased error rate, we use adaptively controlled FEC code. Our simulation study results show that the proposed scheme can increase the network coding gain compared to existing schemes.