Algebraic Codes and Geometry of Some Classical Generalized Polygons

Some results about the geometry of, and the q-ary codes associated with the finite generalized polygons W (q), q = 2n; H (q), q = 3n; and O(q), q = 22m+1, are surveyed to put in context a few simple observations and state a few related questions. In Sect. 4, using the polarity in the case of W (q), q = 22m+1, and that of H (q), q = 32m+1, we present a nondegenerate symmetric bilinear form on, and a polarity of, the q-ary code associated with each of these geometries which is stabilized by the centralizer of the polarity in the automorphism group of the geometry. © Springer India 2014.