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 ε k g r of an orthogonal Grassmannian Δ k . More precisely, we consider the codes arising from the projective system determined by ε k g r ( Δ k ) and determine some of their parameters. We also investigate special sets of points of Δ k which are met by any line of Δ k in at most 2 points proving that their image under the Grassmann embedding is a projective cap.