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This paper focuses on a multicarrier direct-sequence code-division multiple-access system using frequency spread coding, which was proposed by Matsutani and Nakagawa in 1999. Although this system is attractive due to its inherent frequency diversity gain without time or frequency redundancy, it is disadvantaged by its exponential complexity in the maximum likelihood sequence decoding (MLSD). To cope with such a bottleneck, this paper proposes a fast MLSD method which consists of a searching process along the eigenvectors of a symmetric matrix and a refining process. The fast MLSD method is compared with the normal MLSD method via theoretical analysis and simulation results.