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In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.