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It has been proved that when the transmit power is sufficiently large distributed space time codes can achieve the maximal diversity order in a wireless relay network. In the previous works, space time codes used in a wireless relay network are limited on unitary space time codes or orthogonal (or quasi- orthogonal) space time codes. In this paper, we apply general multi-layer full-rate space time codes generated by algebraic extension into the wireless relay network. Moreover, the optimal power allocation and the Chernoff upper bound of the pair-wise error probability (PEP) based on the maximum-likelihood (ML) decoding are calculated. Based on this bound, two design criteria of the multi-layer full-rate space time codes are provided.