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A finite-state code (FSC) is the set of output sequences of a finite-state encoder. The case is considered where the period of the eneoder is one and the code is used as an error-correcting code. In this context the Levenshtein distance will measure the discrepancy between an information sequence and its estimate, and the minimum Hamming distance will be taken as the criterion of efficiency. The class of binary autocomplementary FSC's (BAC's) satisfies a lower bound on the minimum Hamming distance that is essentially equivalent to the well-known Gilbert bound for block codes. Examples of good BAC's are provided in the last section.