Minimum distance of symplectic Grassmann codes

In this paper we introduce symplectic Grassmann codes, in analogy to ordinary Grassmann codes and orthogonal Grassmann codes, as projective codes defined by symplectic Grassmannians. Lagrangian–Grassmannian codes are a special class of symplectic Grassmann codes. We describe all the parameters of line symplectic Grassmann codes and we provide the full weight enumerator for the Lagrangian–Grassmannian codes of rank 2 and 3.