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In this paper, we investigate the secrecy rate of finite alphabet communications over multiple-input, multiple-output, multiple-antenna eavesdropper (MIMOME) systems. Traditional precoder designs at the transmitter for achieving secrecy capacity (maximum secrecy rate) for MIMOME systems are developed according to the assumption of Gaussian input signals. Such designs may risk substantial secrecy rate loss when Gaussian inputs are replaced by practical finite alphabet inputs. To address this issue, we propose a linear precoding design to directly maximize the secrecy rate for MIMOME systems under the constraint of finite alphabet input. Exploiting convex optimization and matrix calculus, we present necessary conditions required of the optimal precoding design and develop an iterative algorithm for finding an efficient precoder. With finite alphabet input signals, maximum transmission power no longer corresponds to maximum secrecy rate as in the case of Gaussian input. We further derive closed-form results on the optimal transmission design for maximizing secrecy rate in low signal-to-noise ratio (SNR) region and near-optimal transmission power in a high SNR region.