On the Rank of Incidence Matrices for Points and Lines of Finite Affine and Projective Geometries over a Field of Four Elements

摘要

We consider incidence matrices for points and lines of affine and projective geometries over a field of four elements. For such matrices we derive a simple formula for the 2-rank and, as a consequence, new combinatorial identities expressing the relation of the obtained formulas for the rank with previously known formulas. We also present a way to construct generating systems for rows of these matrices.