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Network coding has the potential to greatly improve the throughput of wireless networks. In the current proposals for wireless network coding, network nodes transmit packets at a fixed transmission rate. It is notable, however, that by dynamically selecting the rate, we can effectively improve the node transmission efficiency. In this paper, we study the application of a rate-adaptive transmission mechanism in network-coding-based multihop wireless networks. In such networks, whether a coding solution is satisfactory or not depends not only on the number of involved native packets but on the packet loss probabilities of its intended next hops and its transmission time as well, both of which depend on the transmission rate. Therefore, we aim to jointly design the coding operation and rate selection to maximize the transmission efficiency. Specifically, we first describe and mathematically formulate the optimal packet coding and rate-selection problem. Then, we prove the NP-completeness of this optimization problem. Finally, we propose an efficient algorithm for finding good combinations of the coding solution and the transmission rate. Simulation results demonstrate that compared with the rate-fixed transmission, the rate-adaptive transmission based on our algorithm can significantly improve the node transmission efficiency.