Subspace codes from Ferrers diagrams

Abstract: In this paper we give new constructions of Ferrer diagram rank metric codes, which achieve the largest possible dimension. In particular, we prove several cases of a conjecture by T. Etzion and N. Silberstein. We also establish a sharp lower bound on the dimension of linear rank metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters.