# Definition:Hamming Distance

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## Definition

Let $u$ and $v$ be two codewords of a linear code.

The **Hamming distance** between $u$ and $v$ is the number of corresponding terms at which $u$ and $v$ are different.

## Examples

### Codewords in $\map V {4, 3}$

In the master code $\map V {4, 3}$, the Hamming distance between the codewords $1201$ and $2211$ is $2$.

### Codewords in $\map V {4, 2}$

The Hamming distance between the codewords $0101$ and $1110$ is $3$.

## Also known as

The **Hamming distance** is also known as the **Hamming metric**.

Some do not give it a particular name, but merely refer to it as the **distance between codewords**.

## Also see

- Results about
**Hamming distance**can be found**here**.

## Source of Name

This entry was named for Richard Wesley Hamming.

## Sources

- 1996: John F. Humphreys:
*A Course in Group Theory*... (previous) ... (next): Chapter $6$: Error-correcting codes: Definition $6.5$ - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Hamming distance (Hamming metric)** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**distance between two codewords**