Minimum distance of Symplectic Grassmann codes

TL;DR

This paper introduces Symplectic Grassmann codes, analyzes their properties, and determines the minimum distance for line codes, expanding the understanding of projective codes derived from symplectic geometries.

Contribution

It defines Symplectic Grassmann codes, describes their weight enumerator for specific cases, and calculates the minimum distance for line codes, advancing coding theory in symplectic geometry.

Findings

Weight enumerator for rank 2 and 3 Lagrangian-Grassmannian codes

Minimum distance of line Symplectic Grassmann codes determined

Extension of orthogonal Grassmann codes to symplectic setting

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.