An asynchronous cooperative network where different time delays exist among nodes is considered in this paper. Assuming the signals are OFDM modulated, it is first shown that the diversity-multiplexing tradeoff (DMT) achieved by the non-orthogonal selection decode-and-forward (NSDF) protocol for this network is the same as that for the synchronous one. In contrast to the complicated approximately universal "matrix" codes, where each relay uses a different codebook, a systematic construction of an extremely simple "vector" code is proposed. Given the transmitted codeword vector, this vector will be used by all nodes in the network for signal transmission; hence, the proposed coding scheme greatly reduces the complexity of relay deployment and decoding. Furthermore, it is proven that the proposed scheme is optimal in terms of the DMT of the NSDF protocol for this asynchronous network, provided all time delays are distinct. Finally, it is shown that the proposed code design can be extended to the orthogonal selection decode-and-forward protocol and remains to be DMT optimal.