Line Hermitian Grassmann Codes and their Parameters

Abstract

In this paper we introduce and study line Hermitian Grassmann codes as those subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order. In particular, we determine their parameters and characterize the words of minimum weight for $m\ne 5$.

We added to the original paper a corrigendum for the case $m=5$

References in corpus (8)

• Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes
• Automorphism groups of Grassmann codes
• Codes and caps from orthogonal Grassmannians
• Minimum distance of Symplectic Grassmann codes
• Minimum distance of Line Orthogonal Grassmann Codes in even characteristic
• Line Hermitian Grassmann Codes and their Parameters
• On transparent embeddings of point-line geometries
• Enumerative Coding for Line Polar Grassmannians with applications to codes

Cited by in corpus (3)

• Line Hermitian Grassmann Codes and their Parameters
• Implementing Line-Hermitian Grassmann codes
• Linear codes arising from the point-hyperplane geometry-Part I: the Segre embedding