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In this paper, Byzantine attacks in wireless sensor networks with mobile access (SENMA) points is considered, where a portion of the active sensors are compromised to send false information. One effective method to combat with Byzantine attacks is the q-out-of-m scheme, where the sensing decision is based on q sensing reports out of m polled nodes. In this paper, first, by exploiting the approximately linear relationship between the scheme parameters and the network size, we propose a simplified q-out-of-m scheme which can greatly reduce the computational complexity, and at the same time keeping good performance. We show that for a fixed percentage of malicious sensors, the detection accuracy of the simplified q-out-of-m scheme increases almost exponentially as the network size increases. Second, we propose a simple but effective method to detect the malicious sensors before decision making. The performance of the proposed approach is evaluated under both static and dynamic attacking strategies. It is observed that with the pre-detection procedure, the performance of the q-out-of-m scheme can be improved significantly under various attacking strategies. Simulation results are provided to illustrate the effectiveness of the proposed approaches.