Coding theory MOC

Hamming distance

Let be an arbitrary set. The Hamming distance of is the number of positions in which they differ, #m/def/code i.e.

where we have used an Iverson bracket. This defines a metric on .

• A Hamming ball is a closed ball under this metric.
• The distance of a word from a distinguished word is called the Hamming weight, or just weight, which sees a generalization in the linear case to Generalized Hamming weight.

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