Minimum distance of Symplectic Grassmann codes

Abstract

We introduce the Symplectic Grassmann codes as projective codes defined by symplectic Grassmannians, in analogy with the orthogonal Grassmann codes introduced in [4]. Note that the Lagrangian-Grassmannian codes are a special class of Symplectic Grassmann codes. We describe the weight enumerator of the Lagrangian--Grassmannian codes of rank $2$ and $3$ and we determine the minimum distance of the line Symplectic Grassmann codes.

Revised contents and biblography

References in corpus (3)

• Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes
• Codes and caps from orthogonal Grassmannians
• Enumerative Coding for Line Polar Grassmannians with applications to codes

Cited by in corpus (6)

• Minimum distance of Line Orthogonal Grassmann Codes in even characteristic
• Line Hermitian Grassmann Codes and their Parameters
• Enumerative Coding for Line Polar Grassmannians with applications to codes
• Implementing Line-Hermitian Grassmann codes
• Affine Hermitian Grassmann Codes
• Linear codes arising from the point-hyperplane geometry-Part I: the Segre embedding