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Distributed space-time coding was proposed to achieve cooperative diversity in wireless relay networks, in which antennas of relays work as transmit antennas of the sender and generate a space-time code at the receiver in a distributive way. It was proved that this scheme achieves the maximum diversity R when the total transmit power is infinitely large, where R is the number of relays in the network. This paper is on the design of practical distributed space-time codes for wireless relay networks. We use orthogonal and quasi-orthogonal designs which are originally used in the design of space-time codes for multiple-antenna systems. It is well known that orthogonal space- time codes have full diversity and linear decoding complexity. They are particularly suitable for transmissions in the network setting using distributed space-time coding since their 'scale-free' property leads to good performance. Our simulations show that they achieve lower error rates than the random code. We also compare the performance of distributed space-time coding to that of selection decode-and-forward using the same orthogonal designs. Simulations show that distributed space-time coding achieves higher diversity than selection decode-and-forward when there are more than one relay node.