Schubert Subspace Codes

TL;DR

This paper introduces Schubert subspace codes, a new class of geometric codes within Schubert varieties, providing constructions for maximum size codes with optimal minimum distance and exploring generalizations for various distances.

Contribution

It pioneers the study of subspace codes restricted to Schubert varieties, offering geometric constructions for optimal codes and extending the framework to different minimum distances.

Findings

Constructed maximum size codes in certain Schubert varieties.

Achieved the largest possible minimum subspace distance.

Generalized the problem to various minimum distances.

Abstract

In this paper, we initiate the study of constant dimension subspace codes restricted to Schubert varieties, which we call Schubert subspace codes. These codes have a very natural geometric description, as objects that we call intersecting sets with respect to a fixed subspace. We provide a geometric construction of maximum size constant dimension subspace codes in some Schubert varieties with the largest possible value for the minimum subspace distance. Finally, we generalize the problem to different values of the minimum distance.