Walsh codes are perfectly orthogonal binary (antipodal) block codes that found many popular applications over several decades including synchronous multicarrier communications. It is well known that they perform poorly for asynchronous multiuser communications. Therefore, the Gold codes with their superior performance are the preferred user codes in asynchronous CDMA communications. In this paper, new sets of binary orthogonal and near orthogonal user codes are searched in the binary sample space and introduced for asynchronous spread spectrum multicarrier communications. It is shown that the proposed binary user code family outperforms the Walsh codes significantly and they match in performance with the popular, nearly orthogonal Gold codes closely for asynchronous multiuser communications in AWGN channels. On the other hand, we also observed that all the binary codes considered in this study performed comparable for Rayleigh flat fading channels except the inferior performance of Gold codes in synchronous case with high SNR. We present that there are a number of such new binary code sets with different lengths available in the binary sample space. They might help us to improve the multicarrier performance of future communications systems.