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Linear receivers, due to their simpler decoding in comparison with maximum likelihood (ML) receiver, are of great importance. In recent years, the codes such as Toeplitz codes, overlapped Alamouti codes (OACs), and group orthogonal Toeplitz codes (GOTCs) are designed based on the linear receivers decoding. This paper completely explains the zero-forcing (ZF) and the minimum mean square error (MMSE) receivers of the OACs for different numbers of transmit antennas and different numbers of used symbols in each space-time matrix code. It also proposes a method that decreases the complexity of the ZF and the MMSE linear receivers of the OACs without sacrificing the system performance. It is explained that the proposed simplicity method especially gets very effective by increasing the symbol transmission rate.