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In this paper we investigate linear
error correcting codes and projective caps related
to the Grassmann embedding εkgr
of an orthogonal Grassmannian Δk.
In particular,
we determine some of the parameters of the codes arising
from the projective system determined by
εkgr(Δk).
We also study
special sets of points of Δk which are met
by any line of Δk in at most 2 points and we show
that their image under the Grassmann embedding εkgr
is a projective cap
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