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We present a dual-function radar communication (DFRC) system applying signal embedding through a code shift keying (CSK) strategy. The information symbol is phase encoded into a sequence and then modulated by the continuous phase modulation (CPM) before embedding into frequency hopping (FH) radar sub-pulses. The CPM modulated communication symbol phase coded sequence is multiplied with the FH radar waveforms in fast-time and transmitted through multiple-input multiple-output (MIMO) radar platforms. We address the problem of range sidelobe modulation (RSM) and propose the design of the optimum CSK sequences to reduce the degree of change in the range sidelobe levels (RSLs) of the ambiguity function (AF). It is shown that the optimum CSK sequences yield significant reduction in the RSLs of the DFRC system. They also maintain the same degree of correlation between FH sub-pulses regardless of the communication symbol sequences embedded. Additionally, the proposed DFRC system with the optimized waveform design provides good spectrum containment and achieves high communication data rates.