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In most of the existing space-time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang-Liu-Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang-Liu-Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space-time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2times2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4.