Codes and caps from orthogonal Grassmannians

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding εkgr of an orthogonal Grassmannian ΔkΔk. In particular, we determine some of the parameters of the codes arising from the projective system determined by εkgr(Δk). We also study special sets of points of ΔkΔk which are met by any line of ΔkΔk in at most 2 points and we show that their image under the Grassmann embedding εkgr is a projective cap.