Research Projects

Let f be a symplectic form (that is, a nondegenerate alternating bilinear form) on a vector space V of dimension 2n over a finite filed of even order q and let W(2n-1,q) be the corresponding symplectic geometry of rank n. Thus W(2n-1,q) is the point-line geometry whose points are all the points of the projective space PG(2n-1,q) of dimension 2n-1 (associated with $V$) and lines are those lines of PG(2n-1,q) which are totally isotropic with respect to f. In this project, we shall investigate the following linear codes associated with the symplectic geometry W(2n-1,q): (1) the code generated by the hyperbolic lines of W(2n-1,q) and its dual code, (2) the code generated by the lines of W(2n-1,q) and its dual code, and (3) the code generated by the elliptic quadrics of W(2n-1,q) and its dual code.