Subspace codes from Ferrers diagrams

Abstract

In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give 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. We also apply results from algebraic geometry to the study of the analogous problem over an algebraically closed field, proving that the bound by Etzion and Silberstein can be improved in this case, and providing a sharp bound for full-rank matrices.