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We introduce in this paper a new family of space-time codes. These codes are linear, thus they can be decoded via the sphere decoding algorithm or any interference cancellation algorithm. They are full rate, meaning that the system transmits M information symbols per channel use, M being the number of transmit antennas. They are also fully diverse, and information lossless. Thus, the new family of spacetime codes presented here appears as a well-suited solution for high data rate transmission systems.