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The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes (?Perfect space-time block codes.? F. Oggier et al., Trans. Inf. Theory, vol. 52, no. 9, pp. 3885-3902, Sep. 2006), for which the complexity of maximum-likelihood (ML) decoding is considerable. Code diversity is an alternative and complementary approach where a small number of feedback bits are used to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where channel state information (CSI) is used to instruct the transmitter how to choose the code. This method of feedback provides gains associated with beamforming while minimizing the number of feedback bits. Thus, code diversity can be viewed as the integration of space-time coding with a fixed set of beams. It complements the standard approach to code design by taking advantage of different (possibly equivalent) realizations of a particular code design. Feedback can be combined with suboptimal low-complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal. The values of code diversity is verified in the simulations on 4 ? 4 quasi-orthogonal space-time block code (QOSTBC), multi-user detection of Alamouti signaling and the Golden code. It shows that our code diversity scheme is more robust in the case of erroneous feedback compared with other low-rate feedback schemes such as transmit antenna selection and its variations. This paper introduces a family of full rate circulant codes which can be linearly decoded by Fourier decomposition of circulant mat- rices within the code diversity framework.