= Ternary Hamming code
{title2=$[(3^s-1)/2,(3^s-1)/2-s,3]_3$}
For $s\geq2$, use one nonzero representative from each one-dimensional subspace of $\mathbb F_3^s$ as a <parity-check matrix> column. The <rank> is $s$; no zero or proportional columns imply <minimum Hamming distance> at least three. Two independent columns and the representative of their sum give a weight-three relation, proving equality. Every nonzero <syndrome> uniquely identifies one column and one nonzero error value.
Back to article page
