In this paper, a new large spreading code set with a uniform low cross-correlation is proposed. The proposed code set is capable of (1) increasing the number of assigned user (capacity) in a multicarrier code division multiple access (MC-CDMA) system and (2) reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system. In this paper, we derive a new code set and present an example to demonstrate performance improvements of OFDM and MC-CDMA systems. Our proposed code set with code length of N has K=2N+1 number of codes for supporting up to (2N+1) users and exhibits lower cross correlation properties compared to the existing spreading code sets. Our results with subcarrier N=16 confirm that the proposed code set outperforms the current pseudo-orthogonal carrier interferometry (POCI) code set with gain of 5dB at bit-error-rate (BER) level of 10^-4 in the additive white Gaussian noise (AWGN) channel and gain of more than 3.6dB in a multipath fading channel.