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This paper examines the performance of space- time trellis codes (STTCs) over block Rayleigh fading channels with receive antenna selection. Antenna selection is performed based on maximizing the instantaneous received signal-to-noise ratio (SNR). We derive explicit upper bounds on the pairwise error probability and show that the resulting diversity order deteriorates with antenna selection and becomes a function of the number of selected antennas. We provide numerical examples and simulation results that validate these theoretical findings. We remark that the same result holds for fast fading channels, as well as for quasi-static fading channels when the underlying STTC is rank deficient. However, when the channel is quasi-static fading and the STTC is full rank, the diversity order is maintained with antenna selection. In contrast, when the underlying code is an orthogonal space-time block code (OSTBC), the diversity order is always maintained with antenna selection regardless of the type of fading involved. The same results hold when the OSTBC is concatenated with an outer channel code. These findings render STTCs when antenna selection is employed unattractive.