In this paper, a design method is developed for the class of linear-dispersion (LD) codes - a diverse set of space-time codes that subsumes several standard designs. The development begins by showing that for systems that employ a large number of transmit antennas, LD codes constructed from unitary coding matrices are asymptotically optimum from different design perspectives, viz., minimum mean square error (MMSE), mutual information, and average pairwise error probability (PEP). Those measures have a direct impact on the detection complexity, data rate, and error performance that a space-time code can achieve. Using the insight generated by the asymptotic result, a structured design technique for the LD coding matrices, that suits a broad class of configurations is provided. The resulting codes can support high data rates and provide performance advantages over current designs when decoded with a standard detector. Based on the asymptotic results, a row interleaving scheme is proposed, and it is shown to result in significant performance enhancement.