A k-polar Grassmannian is a 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 μ 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 μ to be 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 either type.

Cardinali, I., Giuzzi, L. (2017). Enumerative coding for line polar Grassmannians with applications to codes. FINITE FIELDS AND THEIR APPLICATIONS, 46, 107-138 [10.1016/j.ffa.2017.03.005].

Enumerative coding for line polar Grassmannians with applications to codes

CARDINALI, ILARIA
;
2017-01-01

Abstract

A k-polar Grassmannian is a 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 μ 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 μ to be 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 either type.
Cardinali, I., Giuzzi, L. (2017). Enumerative coding for line polar Grassmannians with applications to codes. FINITE FIELDS AND THEIR APPLICATIONS, 46, 107-138 [10.1016/j.ffa.2017.03.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1006621