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

Abstract

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 gr k of an orthogonal Grassmannian ∆ k . More precisely, we consider the codes arising from the projective system determined by ε gr 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.