NP-hardness conjecture for deciding deep holes of Gabidulin codes

Let a Gabidulin code be given together with a received word. A received word is a deep hole if its distance from the code equals the covering radius. NP-hardness conjecture. Deciding whether a received word is a deep hole of the Gabidulin code is NP-hard. The paper presents a necessary and sufficient condition for deciding deep holes and conjectures that the resulting decision problem is computationally intractable, analogously to the corresponding problem for generalized Reed–Solomon codes, which is known to be NP-hard.