Generalizing Subspace Codes to Flag Codes Using Group Actions

Abstract

In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.