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

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].
File in questo prodotto:
File Dimensione Formato  
Cardinali-2017-Enumerative-coding-for-line-polar-g.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 558.08 kB
Formato Adobe PDF
558.08 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/1006621