Reconfigurable error-correcting codes beyond the Hadamard code

Identify error-correcting codes enc that are (δ, μ)-reconfigurable in the sense that, for any distinct messages α and β, there exists a reconfiguration sequence from enc(α) to enc(β) such that every intermediate function is δ-close to either enc(α) or enc(β) and (δ+μ)-far from enc(γ) for all γ distinct from α and β.

Background

The paper proves a reconfigurability property for Hadamard codes and leverages it to achieve robustization in the alphabet-reduction step for Maxmin Binary CSP Reconfiguration.

The authors ask whether similar reconfigurability properties exist for other error-correcting codes, formalizing a notion of (δ, μ)-reconfigurability that would generalize their technique beyond the Hadamard code.