Hamming code of length seven
= Hamming code of length seven
{c}
{title2=$[7,4,3]$}
The <binary linear code> known as the <Hamming code> of length seven is the <kernel> of a $3\times7$ <parity-check matrix> whose columns are all the nonzero vectors of $\mathbb F_2^3$. Its <dimension> is four. No one-column or two-column sum vanishes, but some three-column sum does, so its <minimum Hamming distance> is three. The <syndrome> of a one-bit error is its column, uniquely identifying the erroneous position.