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We design novel space-time multipath (STM) coded multi-antenna transmissions over frequency-selective Rayleigh fading channels. We develop STM coded systems that guarantee the maximum possible space-multipath diversity, along with large coding gains, and high bandwidth efficiency for any number of transmit-receive antennas. By incorporating subchannel grouping, we also enable desirable tradeoffs between performance and complexity. Our designs rely on digital phase sweeping or block circular delay operations and apply to both single- and multi-carrier systems. Their merits are confirmed by corroborating simulations and comparisons with existing approaches.