The Hamming space of length over a finite field is the set equipped with Hamming distance, the number of coordinates at which two words differ. The Hamming weight of a word is its distance from zero.
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Hamming space is a mathematical concept used primarily in coding theory and information theory. It refers to the set of all possible strings of a fixed length over a specified alphabet, usually binary (0s and 1s). The term "Hamming space" is often associated with Hamming distance, which quantifies the difference between two strings of equal length.