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It is shown that single symbol maximum-likelihood (ML) decoding for chosen rate 6/8 linear complex space-time codes for up to eight transmit antennas is possible in the presence of a phase feedback. The performance of the code is the same as that of an ideal code, for which the sufficient statistic of the channel is its Frobenius norm. For rate 1 codes for up to eight antennas, a two-phase feedback enables a symbol to see the interference from only one symbol instead of three, thereby reducing the complexity of ML decoding. Quantization of the feedback is also considered.