Codes Associated with Nondegenerate Quadrics of a Symplectic Space of Even Order

This paper studies the incidence relation between the points and quadrics in the projective space of a symplectic vector space over a field of even order. The 2-rank of the incidence matrix is determined. This is achieved by viewing the code generated by incidence vectors as a module for the symplectic group and applying the 2-modular representation theory of this group. The radical series of this module is also described.