Codes and caps from orthogonal Grassmannians

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