Codes and caps from orthogonal Grassmannians

Abstract

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