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The minimum distance is the fundamental performance parameter for modems using maximum likelihood sequence estimation (MLSE). This paper provides a procedure for finding the minimum distance for classes of systems of moderate complexity, e.g., with a few hundred states. This is done by applying various rules which reduce the set of error sequences that have to be considered to a small number. Nulls in the channel's frequency spectrum reduce the number of critical error sequences still further. Examples using the procedure are given for many classes of responses of interest. It is also noted that the optimum transmitter design problem is a convex programming problem.