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MENTAL MODEL · M4571

Hamming Distance

Hamming Distance
Learn & MetacognitionHigh supportCognitive Science
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other. The Hamming weight is the Hamming distance between a string and the zero string of the same length, that is, the number of non-zero elements in the string: for binary strings, it is the number of 1s, so the Hamming weight of 11101 is 4.

SCAFFOLDING EFFECT

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In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other. The Hamming weight is the Hamming distance between a string and the zero string of the same length, that is, the number of non-zero elements in the string: for binary strings, it is the number of 1s, so the Hamming weight of 11101 is 4.

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For two strings of equal length, count the number of positions where they differ; this count is the distance. A code with minimum distance d can detect up to d-1 errors and correct up to floor((d-1)/2) errors. It quantifies "difference" as the minimum number of flips required, forming the geometric basis for error-correcting code design.

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Source support: Explicit

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