Coding theory MOC

Hamming distance

Let be an arbitrary set. The Hamming distance of is the number of positions in which they differ, 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.

---

tidy | en | sembr