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MIMO systems with perfect channel state information at both sides of the link can adapt to the instantaneous channel conditions to optimize the spectral efficiency and/or the reliability of the communication. A low-complexity approach is the use of linear MIMO transceivers which are composed of a linear precoder at the transmitter and a linear equalizer at the receiver. The design of linear transceivers has been extensively studied in the literature with a variety of cost functions. In this paper, we focus on the minimum BER design, and show that the common practice of fixing a priori the number of data symbols to be transmitted per channel use inherently limits the diversity gain of the system. By introducing the number of symbols in the optimization process, we propose a minimum BER linear precoding scheme that achieves the full diversity of the MIMO channel. For the cases of uncorrelated/semicorrelated Rayleigh and uncorrelated Rician fading, the average BER performance of both schemes is analytically analyzed and characterized in terms of two key parameters: the array gain and the diversity gain.