Hamming space

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Hamming space In coding theory, a mathematical space in which words of some given length may be situated, the separation of points in the space being measured by the Hamming distance. The dimensionality of the space is equal to the number of digits in the words; the coordinate in each dimension is given by each successive digit in the words.

The Hamming sphere is the set of all words in Hamming space whose Hamming distance from some given word (the “center”) does not exceed some given value (the Hamming radius).