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Code diversity using space-time block codes was developed for single-carrier and single-receiver systems. In this paper, the extension of code diversity by phase rotation to multi-user and multi-carrier systems is proposed and analyzed. We show that code diversity with reduced feedback is possible in this new scenario and the coding gain has a mild logarithmic decrease with the number of users and the number of sub-carriers. In addition, we develop an analytical upper bound for the average error probability whose accuracy is verified by simulation.