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Enumerative Coding for Line Polar Grassmannians with applications to codes
A -polar Grassmannian is the geometry having as pointset the set of all
-dimensional subspaces of a vector space which are totally isotropic for
a given non-degenerate bilinear form defined on Hence it can be
regarded as a subgeometry of the ordinary -Grassmannian. In this paper we
deal with orthogonal line Grassmannians and with symplectic line Grassmannians,
i.e. we assume and 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.Comment: 27 pages; revised version after revie