Subcode distances for non-Gabidulin MRD codes

Characterize the behavior of subcode distances under the Add-and-Remove construction when the original code is an MRD code that is not a Gabidulin code.

Background

The main exact results for subcode distances rely on the explicit subcode-distance profile and nested subcodes of matrix Gabidulin codes. The paper does not establish whether analogous preservation and one-unit-decrease phenomena hold for MRD codes lacking Gabidulin structure, leaving their behavior under Add-and-Remove transformations unresolved.

References

Several questions remain open: how often the decrease at the exceptional indices occurs, in particular for the $MIRANDA$ parameters, what happens for MRD codes that are not Gabidulin codes, and whether subcode distances can be used in a polynomial-time distinguisher.

— Code distances of matrix rank-metric codes under Add-and-Remove transformations  (2610.03460 - Alfarano et al., 2 Oct 2026) in Section 1, Introduction

Several questions remain open: how often the decrease at the exceptional indices occurs, in particular for the $MIRANDA$ parameters, what happens for MRD codes that are not Gabidulin codes, and whether subcode distances can be used in a polynomial-time distinguisher. The last question requires knowledge of the subcode distances of random matrix codes, which we leave for future work.

— Code distances of matrix rank-metric codes under Add-and-Remove transformations  (2610.03460 - Alfarano et al., 2 Oct 2026) in Section 1, Introduction