Definition:Hamming Distance
(Redirected from Definition:Hamming Metric)
Jump to navigation
Jump to search
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