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In this paper, we propose a generic method to construct group-decodable space-time block codes (STBC) with arbitrary code dimensions, including odd time slot. Based on the proposed code construction method, 3-time-slot STBC for two transmit antennas with full or even higher code rate can be obtained. The full-rate 3-time-slot STBC obtained can achieve full diversity and symbol-wise decoding complexity. It serves as a solution to the orphan-symbol (3-time-slot) transmit diversity issue raised in 3rd Generation Partnership Project (3GPP) standards.