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We consider a flat fading wireless link having multiple M transmitter antennas and a single receiver antenna (MISO). This system is often useful in mobile downlink communications for which the mobile receiver may not be able to support multiple antennas. For such a system, we propose a novel and very simple design of full diversity two-group and four-group decodable block diagonal linear dispersion codes with rate one for any number of the transmitter antennas. For M = 2n and M = 2n - 1, we also prove that for K-say quadrature amplitude modulation (QAM) transmission equipped with a maximum likelihood (ML) detector, our proposed code minimizes the worst case average pair-wise error probability, i.e., it achieve optimal coding gain.