Constructions of multiblock space-time coding schemes that are optimal with respect to diversity-multiplexing (D-M) tradeoff when coding is applied over any number of fading blocks are presented in this correspondence. The constructions are based on a left-regular representation of elements in some cyclic division algebra. In particular, the main construction applies to the case when the quasi-static fading interval equals the number of transmit antennas, hence the resulting scheme is termed a minimal delay multiblock space-time coding scheme. Constructions corresponding to the cases of nonminimal delay are also provided. As the number of coded blocks approaches infinity, coding schemes derived from the proposed constructions can be used to provide a reliable multiple-input multiple-output (MIMO) communication with vanishing error probability.