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General expressions for the probability of word error for several encoding/detection schemes using group codes are derived. Correlation detection, digital decoding, straight Wagner codes, "Wagnerized" codes, and direct transmission are covered. Specific results are given for each in the case where the additive channel noise is white and Gaussian. A good indication of the relative amounts of power required by two schemes operating at the same error rate is available from an asymptotic relationship as the signal-to-noise ratio approaches infinity. Numerical results are presented for three easily implemented codes.