In this paper, a systematic construction of asymmetric space-time codes that is a promising solution to the asymmetric coding problem is presented. By the asymmetric coding problem we mean that the number of receive antennas is strictly less than the number of transmit antennas in a MIMO communication system, and the task is to design a coding scheme that has an efficient decoding using e.g. a sphere decoder. Specifically, given any desired antenna selection pattern, the proposed construction will yield codes that are transmitted using exactly the specified pattern, and that can be easily decoded using sphere decoding or MMSE techniques. Our construction can be applied to any kinds of antenna selection patterns, including the one that equally-likely uses all possible n-subsets of the transmit antennas for some n. Moreover, the resulting codes are proved to achieve the diversity-multiplexing tradeoff associated with the designated selection pattern.