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 [Cardinali, I., and L. Giuzzi, Caps and codes from orthogonal Grassmannians, submitted], on projective caps and linear error correcting codes arising from the Grassmann embedding of an orthogonal Grassmannian Δk. More precisely, we consider the codes arising from the projective system determined by and determine some of their parameters. We also investigate special sets of points of Δk which are met by any line of Δk in at most 2 points proving that their image under the Grassmann embedding is a projective cap.