  A $k$-polar Grassmannian is the geometry having as pointset the set of all
$k$-dimensional subspaces of a vector space $V$ which are totally isotropic for
a given non-degenerate bilinear form $\mu$ defined on $V.$ Hence it can be
regarded as a subgeometry of the ordinary $k$-Grassmannian. In this paper we
deal with orthogonal line Grassmannians and with symplectic line Grassmannians,
i.e. we assume $k=2$ and $\mu$ a non-degenerate symmetric or alternating form.
We will provide a method to efficiently enumerate the pointsets of both
orthogonal and symplectic line Grassmannians. This has several nice
applications; among them, we shall discuss an efficient encoding/decoding/error
correction strategy for line polar Grassmann codes of both types.
