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In this paper, we propose to design linear-dispersion (LD) codes by minimizing the union bound based on the exact pairwise error probability (PEP). We find that the original programming is not convex, and we present a convex relaxation to the optimization problem. We employ the gradient descent methods to numerically search the optimum dispersion matrices. Simulation results show that codes optimized by the new criterion generally outperform the codes designed based on algebraic number theory. When the knowledge of spatial-fading correlation is available in advance for the design, significant gain relative to the codes designed without knowledge of channel correlation can be achieved by taking into account the correlation structure while performing the optimization. We demonstrate how to exploit knowledge of transmit and receive correlation in designing the LD codes. Numerical and simulation examples show that knowledge of transmit correlation has a large impact on the optimum performance of the LD codes. Furthermore, additional gain can be achieved from the knowledge of receive correlation.