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A simple half-duplex decode-and-forward relay channel is presented and analyzed. Relays access the common channel by means of a randomized linear-dispersion space-time block code which is flexible with respect to the number of relays and the coding rate α. When the dimensions of the linear dispersion matrices grow large, but with constant ratio α, the spectral efficiency of the system converges fast to a deterministic quantity. Simulation results show that this asymptotic value is an extremely good approximation of the finite reality, even for not-so-large codes. Then, this asymptotic spectral efficiency is used to characterize the outage probability in the high-SNR regime. With maximum-likelihood reception, the proposed randomized coding scheme is shown to achieve full diversity order L+1, with L the total number of relays. On the contrary, with the sub-optimal LMMSE receiver, relays add diversity to the system only if the coding rate is small enough.