Line Hermitian Grassmann Codes and their Parameters

TL;DR

These subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order are introduced and studied.

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 $m\neq5$.