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Antenna selection, as a special case of power adaptation, can enhance the capacity of layered space time codes under rate control without any overhead feedback. To efficiently fight back rates quantization, this contribution considers a joint optimization of the best active transmit antennas associated to rate control together with antenna partitioning (i.e., layered multidimensional coding) and decoding order degrees of freedom. We propose an iterative antenna selection, which initializes the decoding order, so as to keep a low computational complexity while achieving near-optimal performance. Gains get all the more important as the signal-to-noise ratio increases.