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Space time codes seek to exploit the statistical properties of a multi-antenna transmission scenario. We focus on maximizing a codes diversity which is determined by the rank between codeword difference pairs at high SNR. This criterion must be evaluated over a complex modulation alphabet C. Work by Liu et al. (2000) presents a criterion for selecting maximum rank codes over GF(22l) which preserve their rank properties when mapped to QAM modulation. This paper presents a different solution to the problem of coding and modulation. Finite field codes are considered which can be mapped to the complex Gaussian integer field. Any full rank finite code construction will achieve maximum diversity when mapped to the Gaussian integer field.