Orthogonal-design-based space-time (ODST) codes of size (n×n) offer maximum diversity gain advantage and a simple yet optimal decoding algorithm under an arbitrary signal alphabet or constellation A. However, these designs only exist for n=2, 4, 8 when A is real and for n=2 when A is complex. In this letter, we address the question of the existence of ODST codes of other sizes when A is restricted to be a proper subset of either real or complex numbers. We refer to these as restricted-alphabet ODST (RA-ODST) codes. We show that real RA-ODST codes of size greater than 8 that also guarantee maximum diversity advantage do not exist. Without the diversity requirement, RA-ODST codes exist only when A={a,-a}, 0
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