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In this paper, an adaptive distributed space-time block code (ADSTBC) with linear decoding complexity is proposed. Within a group of candidate minimum-decoding-complexity quasi-orthogonal STBC (MDC-QO-STBC) codewords obtained by changing the row order of a basic one, the codeword that has minimum absolute value of interference between real symbols (IRS) in its equivalent channel correlation matrix is optimal and adopted by ADSTBC. In addition, for the optimal codeword's IRS absolute value is small enough to be ignored, linear decoding can achieve the performance of single complex symbol maximum-likelihood decoding, which is employed by MDC-QO-STBC, thus the decoding complexity is significantly reduced. The simulation results when the cooperative relays number is 4 and 3 both show the superiority of ASTBC over the normal DSTBC in the block error ratio performance and decoding complexity as well.