The Hamming (7,4) code is the binary Hamming code 
, with code parameters 
. It encodes four data bits in a seven-bit codeword
and corrects any single-bit error. One parity check
matrix is
![H=[1 0 1 0 1 0 1; 0 1 1 0 0 1 1; 0 0 0 1 1 1 1],](/images/equations/Hamming74Code/NumberedEquation1.svg) |
whose columns are the seven nonzero vectors in the three-dimensional vector space over the two-element finite field. The
codewords are the vectors 
satisfying
 |
The code has minimum Hamming distance 3 and is a perfect code.
