Codes on Linear Sections of Grassmannians

Abstract

We study algebraic geometry linear codes defined by linear sections of the Grassmannian variety as codes associated to FFN$(1,q)$-projective varieties. As a consequence, we show that Schubert, Lagrangian-Grassmannian, and isotropic Grassmannian codes are special instances of codes defined by linear sections of the Grassmannian variety.

13pp