The frame rate in medical ultrasound imaging may be increased significantly by reducing the number of transmit firings per image frame. Cooley et al. (1994) and Lockwood et al. (1995) have described synthetic aperture imaging systems where each frame is imaged using data obtained from a small number of transmit elements fired in succession. These "synthetic transmit aperture" systems have potential for very high frame rates, but they also suffer from low SNR. Here, the authors present a method for increasing the SNR of such systems by using spatially-encoded transmits. The transmitted power is increased by having multiple active transmitters in each firing. The active transmitters are encoded in a spatial code which allows the received data to be subsequently sorted by each transmitter for synthetic aperture beamforming. The authors present the spatial coding and decoding theory and show experimental results to demonstrate its application.