Codes associated with nondegenerate quadrics of a symplectic space of even order

摘要

This paper studies the incidence relation between the points and quadrics in the projective space of a symplectic vector space over a field oi 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. (C) 2001 Academic Press. [References: 15]