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Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.
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Incidence matrices of generalized quadrangles
You can compute them with the FinInG package in the computer algebra system GAP. FinInG has available all the classical generalised quadrangles, elation generalised quadrangles (with a $q$-clan, flock …