Line Polar Grassmann Codes of Orthogonal Type

2014/07/23 by Ilaria Cardinali, Cardinali, Ilaria, Luca Giuzzi +3 · 2 citations
Computer Science · Mathematics · #51A45 #51A50 #51E22 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Mathematics #math.CO #msc:51A45 #msc:51A50 #msc:51E22

paper · pdf · doi:10.48550/arxiv.1407.6149

openalex publication_date 2014/07/23 · arxiv created 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, Codes and caps from orthogonal Grassmannians, Finite Fields Appl. \bf 24 (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Plücker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for q odd.

Citations

• Automorphism groups of Grassmann codes

Cited by

• On minimal codes arising from projective embeddings of point-line geometries
• Linear codes arising from the point-hyperplane geometry -- Part II: the twisted embedding
• Linear codes arising from the point-hyperplane geometry-Part I: the Segre embedding

Related

• Computing the minimum distance of the C(\mathbbO_3,6) polar Orthogonal Grassmann code with elementary methods
• Polar Grassmannians and their Codes
• Line Hermitian Grassmann Codes and their Parameters
• Affine Hermitian Grassmann Codes
• Affine Symplectic Grassmann codes