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In a dynamic spectrum access (DSA) network, multi-carrier-based cognitive radio transceivers need to deactivate some of their subcarriers to avoid interference to primary users. In a mobile environment, the spread orthogonal frequency-division multiplexing (SOFDM) system has demonstrated excellent performance in multipath fading channels, outperforming the traditional OFDM system due to the diversity gain. The traditional SOFDM uses Hadamard-Walsh code as the spreading code set, in which case, when deactivating subcarriers, orthogonality among different spreading codes will be lost, leading to poor bit error ratio (BER) performance. The performance of the SOFDM system can be improved by using adaptive spreading code adjustment to compensate for the loss of orthogonality. Because Hadamard-Walsh codes only exist for certain code length, in many cases, the SOFDM system based on Hadamard-Walsh code set needs to deactivate more subcarriers. Otherwise, loss of orthogonality cannot be eliminated. Instead, it can only be minimized. Moreover, deactivating more subcarriers will force the system to reduce the data rate. By treating the system as subsystems, we can generate binary orthogonal code set based on Hadamard-Walsh code to maintain the data rate. On the other hand, if the spreading code is not limited to be binary, orthogonal carrier interferometry (CI) codes exist for code length of any integer. Hence, by applying non-contiguous SOFDM (NC-SOFDM) with CI code to DSA, the loss of orthogonality among spreading codes caused by deactivating subcarriers can be eliminated. In this paper, we propose two novel spread coding schemes for NC-SOFDM for cognitive radio in a DSA network. The new spreading code sets help the system to maintain the same data rate as that of the traditional OFDM and improve the performance by exploiting the diversity gain and eliminating the orthogonality loss. The NC-SOFDM with the proposed spreading code outperforms the traditional NC-OFDM and the ad- - aptive NC-SOFDM with Hadamard-Walsh code.