[[Hamming code]]
# $[7,4,3]_{2}$ Hamming code

The $[7,4,3]_{2}$ [[Hamming code]] is the smallest [[perfect code]]. #m/def/code 
It may be thought of as

- The row space of the [[Incidence relation#Incidence matrix]] of the [[Fano plane]] with the $\vab 1$ codeword added.
- The code whose [[Linear code#^check]] consists of the [[homogenous coördinates]] of all points in the [[Fano plane]] as columns.

#
---
#state/develop | #lang/en | #SemBr