Definition:Hamming Distance

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