Codes and caps from orthogonal Grassmannians

In this paper we investigate linear error correcting codes and. projective caps related to the Grassmann embedding epsilon(gr)(k) of an orthogonal Grassmannian Delta(k). In particular, we determine some of the parameters of the codes arising from the projective system determined by epsilon(gr)(k)(Delta(k)). We also study special sets of points of Delta(k) which are met by any line of Delta(k) in at most 2 points and we show that their image under the Grassmann embedding epsilon(gr)(k) is a projective cap. (C) 2013 Elsevier Inc. All rights reserved.