Characterize optimal codes for other irreducible Ferrers diagrams

Determine which irreducible Ferrers diagrams admit optimal Ferrers diagram rank-metric codes, and establish whether the Delsarte dual and puncturing-inclusion techniques used for the diagram \([3,3,3,5]\) can be adapted to other irreducible Ferrers diagrams.

Background

The paper constructs an optimal Ferrers diagram rank-metric code for the irreducible diagram $[3,3,3,5]$ by combining a puncturing-inclusion construction with semifield codes and Delsarte duality. The authors leave unresolved how broadly this approach applies beyond that specific diagram.

The open problem seeks both a classification of irreducible diagrams that admit optimal codes and an assessment of whether the technical methods developed in the paper—particularly Delsarte duality and puncturing-inclusion—can be transferred to those diagrams.