ternary; projective plane; incidence matrix; finite projective plane; ternary ring; system of orthogonal Latin squares; Hall plane of order 9; Hughes plane of order 9
A combinatorial characterization of finite projective planes using strongly canonical forms of incidence matrices is presented. The corresponding constructions are applied to known projective planes of order 9. As a result a new description of the Hughes plane of order nine is obtained.
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