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This paper is focused on the design of the shared signal for a dual-use system with radar detection and communication functions. To achieve a good aperiodic autocorrelation property of the shared signal for radar detection, the lp-norm of the autocorrelation sidelobes is minimized. For a communication function, the nulling of one or more frequency bands enables information to be embedded and an energy minimization detection method is introduced to demodulate communication information. In addition, electromagnetic spectral compatibility and unimodular constraints on the designed signal are considered. The resulting problem is a higher order, multi-dimensional, and multi-objective constrained optimization, which is efficiently handled through an iteration direct search algorithm. Finally, the performance of the proposed method is assessed and analyzed through numerical simulations in terms of the peak sidelobe level, average sidelobe level, and bit error rate.