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 \cite{CG}, on projective caps and linear error correcting codes arising from the Grassmann embedding $\varepsilon_k^{gr}$ of an orthogonal Grassmannian $\Delta_k.$ More precisely, we consider the codes arising from the projective system determined by $\varepsilon_k^{gr}(\Delta_k)$ and determine some of their parameters. We also investigate special sets of points of $\Delta_k$ which are met by any line of $\Delta_k$ in at most $2$ points proving that their image under the Grassmann embedding is a projective cap.