Establishing a radio link in cell-based mobile communication systems involves searching and synchronizing the downlink known pattern of sequences associated with the base stations. The performance of the searching process, often referred to as cell search, depends greatly on the employed preamble sequences. In this paper, we propose a construction of quasi complete complementary codes (QCCCs) from Reed-Muller codes and, due to their good auto-correlation and cross-correlation properties, a preamble structure based on QCCCs. Furthermore, the constructed QCCCs have low peak-to-average power ratios (PAPRs) and hence are suitable for use in orthogonal frequency division multiplexing (OFDM) systems. Simulation results show that the QCCC-based preambles outperform the preambles employed in the WiMAX system, both in terms of PAPR and cell search performance. Moreover, the rich algebraic structures of QCCCs potentially admit low-complexity encoding and decoding.