Ternary dual codes of the planes of order nine (Q5935440)

There exist four projective planes of order nine. They are the desarguesian plane \(\Phi\), the translation (Hall) plane \(\Omega\), the dual translation plane \(\Omega^D\) and the Hughes plane \(\Psi\). The main result of the paper determines the minimum weight of the dual ternary code of such planes. It is \(15\) if the plane is \(\Phi\), \(\Omega\), or \(\Omega^D\) and \(14\) if the plane is \(\Psi\).