Hanani triple packings and optimal \(q\)-ary codes of constant weight three
The exact sizes of optimal \(q\)-ary codes of length \(n\), constant weight \(w\) and distance \(d=2w-1\) have only been determined for \(q\in \{2,3\}\), and for \(w|(q-1)n\) and \(n\) sufficiently large. We completely determine the exact size of optimal \(q\)-ary codes of constant weight three and minimum distance five for all \(q\) by establishing a connection with Hanani triple packings, and settling their existence.
hanani triple packings constant-weight codes hanani triple systems resolvable designs 94b25 05b05 05b40