In mobile wireless networks, the emerging proximity-based applications have led to the need for highly effective and energy-efficient neighbor discovery protocols. However, existing works cannot realize the optimal worst-case latency in the symmetric case, and their performances with asymmetric duty cycles can still be improved. In this paper, we investigate asynchronous neighbor discovery through a code-based approach, including the symmetric and asymmetric cases. We derive the tight worst-case latency bound in the case of symmetric duty cycle. We design a novel class of symmetric patterns called Diff-Codes, which is optimal when the Diff-Code can be extended from a perfect difference set. We further consider the asymmetric case and design ADiff-Codes. To evaluate (A)Diff-Codes, we conduct both simulations and testbed experiments. Both simulation and experiment results show that (A)Diff-Codes significantly outperform existing neighbor discovery protocols in both the median case and worst case. Specifically, in the symmetric case, the maximum worst-case improvement is up to 50%; in both symmetric and asymmetric cases, the median case gain is as high as 30%.