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We propose a blind multiuser detector based on Monte Carlo Markov chain (MCMC) techniques. The detector exploits mutually orthogonal complementary sequences to distinguish between transmitting users and space-time codes to take advantage of the available spatial diversity. We propose a partitioning scheme for the symbol draws in the MCMC algorithm that reduces the complexity without any degradation in performance. The detector's performance is simulated in an iterative receiver that utilizes an outer coder. The simulations display some loss in coding gain because of the blind nature of the system; however, diversity gain is preserved.