We propose a space–time block coding framework based on linear precoding. The codes for $P$ transmit antennas are formed by transmitting the information vector (with $P$ independent information symbols) $L$ times where each time it is rotated by a distinct precoding matrix. The framework generalizes conventional spatial multiplexing techniques and facilitates tradeoff between rate and diversity. We propose a simple construction for precoding matrices whose parameters are chosen to guarantee maximal diversity using algebraic number theory. Our codes exhibit circular structure, which greatly simplifies the performance analysis and facilitates linear decoding. Theoretical analysis and numerical simulations demonstrated excellent performance of the proposed algebraic precoding framework.