Some results on caps and codes related to orthogonal Grassmannians - a preview

In this note we offer a short summary of some recent results, to be contained in a forthcoming paper [4], on projective caps and linear error correcting codes arising from the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. More precisely, we consider the codes arising from the projective system determined by ε k (∆k) and determine some of their parameters. We also investigate special sets of points of ∆k which are met by any line of ∆k in at most 2 points proving that their image under the Grassmann embedding is a projective cap.