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The term minimum distance may refer to

Minimum distance estimation, a statistical method for fitting a model to data
Closest pair of points problem, the algorithmic problem of finding two points that have the minimum distance among a larger set of points
Euclidean distance, the minimum length of any curve between two points in the plane
Shortest path problem, the minimum length of a path between two points in a graph
The minimum distance of a block code in coding theory, the smallest Hamming distance between any two of its code words

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