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Using mutually shift-orthogonal spreading codes, block-spread code-division multiple access (BS-CDMA) systems have been shown to achieve multiuser interference (MUI)-free reception when synchronization between the base station and the subscriber stations is achieved. In practice, when carrier frequency offset (CFO) is present, orthogonality among users is destroyed, and MUI occurs. This paper presents three methods of designing the spreading and despreading codes for uplink BS-CDMA systems to reduce MUI due to CFO. We show through rigorous derivation that all three codes can completely eliminate MUI due to CFO. In particular, by fixing the spreading codes at the transmitter, despreading codes that were obtained by minimizing the interference power or their cross correlation with the spreading codes are shown to yield a performance close to a synchronous system. The advantages and disadvantages of the BS-CDMA systems using the three proposed codes are discussed.