An asynchronous cooperative network where different time delays among nodes exist is considered in this paper. With OFDM modulation, 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 sharp contrast to the currently available complicated approximately universal "matrix" codes, a systematic construction of an extremely simple "vector" code is proposed. Given the transmitted codeword vector, the same codeword will be sent by all nodes during transmission, hence it will greatly reduce the complexities of relay deployment and decoding. Furthermore, it is proved that the proposed scheme achieves the optimal DMT of the NSDF protocol for this asynchronous cooperative network.