Schubert subspace codes

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 name intersecting sets with respect to a fixed subspace. We provide a geometric construction of the 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.