This paper proposes the class of Generalized Least-Square-Error (GLSE) precoders for multiuser massive MIMO systems. For a generic transmit constellation, GLSE precoders minimize the interference at user terminals assuring that given constraints on the transmit signals are satisfied. The general form of these precoders enables us to impose multiple restrictions at the transmit signal such as limited peak power and restricted number of active transmit antennas. Invoking the replica method from statistical mechanics, we study the performance of GLSE precoders in the large-system limit. We show that the output symbols of these precoders are identically distributed and their statistics are described with an equivalent scalar GLSE precoder. Using the asymptotic results, we further address some applications of the GLSE precoders; namely forming transmit signals over a restricted alphabet and transmit antenna selection. Our investigations demonstrate that a computationally efficient GLSE precoder requires $41\%$ fewer active transmit antennas than conventional selection protocols in order to achieve a desired level of input-output distortion.