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Integrated sensing and communication (ISAC) is a key enabling technique for future wireless networks owing to its efficient hardware and spectrum utilization. In this paper, we focus on dual-functional waveform design for a multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) ISAC system, which is considered to be a promising solution for practical deployment. Since the dual-functional waveform carries communication information, its random nature leads to high range-Doppler sidelobes in the ambiguity function, which in turn degrades radar sensing performance. To suppress range- Doppler sidelobes, we propose a novel symbol-level precoding (SLP)-based waveform design for MIMO-OFDM ISAC systems by fully exploiting the available temporal degrees of freedom. Our goal is to minimize the range-Doppler integrated sidelobe level (ISL) while satisfying the constraints of target illumination power, multi-user communication quality of service (QoS), and constant-modulus transmission. To solve the resulting non-convex waveform design problem, we develop an efficient algorithm using the majorization-minimization (MM) and alternative direction method of multipliers (ADMM) methods. Simulation results show that the proposed waveform has significantly reduced range-Doppler sidelobes compared with signals designed only for communications and other baselines. In addition, the proposed waveform design achieves target detection and estimation performance close to that achievable by waveforms designed only for radar, which demonstrates the superiority of the proposed SLP-based ISAC approach.