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.
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|Titolo:||Enumerative coding for line polar Grassmannians with applications to codes|
|Rivista:||FINITE FIELDS AND THEIR APPLICATIONS|
|Citazione:||Cardinali, I., & Giuzzi, L. (2017). Enumerative coding for line polar Grassmannians with applications to codes. FINITE FIELDS AND THEIR APPLICATIONS, 46, 107-138.|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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