Enumerative coding for line polar Grassmannians with applications to codes

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...

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Bibliographic Details
Published in:Finite fields and their applications Vol. 46; pp. 107 - 138
Main Authors: Cardinali, Ilaria, Giuzzi, Luca
Format: Journal Article
Language:English
Published: Elsevier Inc 01.07.2017
Subjects:
Enumerative coding
Linear code
Polar Grassmannian
Enumerative coding
Linear code
14M15
Polar Grassmannian
94B27
94B05
ISSN:1071-5797, 1090-2465
Online Access:Get full text
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Summary: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.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2017.03.005