On the list decodability of rank-metric codes containing Gabidulin codes
Paolo Santonastaso, Ferdinando Zullo

TL;DR
This paper investigates the list decodability of rank-metric codes containing Gabidulin codes, establishing bounds and identifying families that cannot be efficiently decoded for large decoding radii.
Contribution
It provides bounds on list size for such codes and identifies specific families that are not efficiently list decodable, extending previous results.
Findings
Certain rank-metric codes containing generalized Gabidulin codes cannot be efficiently list decoded for large radii.
Identifies families of codes that are not efficiently list decodable.
Provides bounds on list size to determine the existence of polynomial-time list decoding algorithms.
Abstract
Wachter-Zeh in [42], and later together with Raviv [31], proved that Gabidulin codes cannot be efficiently list decoded for any radius , providing that is large enough. Also, they proved that there are infinitely many choices of the parameters for which Gabidulin codes cannot be efficiently list decoded at all. Subsequently, in [41] these results have been extended to the family of generalized Gabidulin codes and to further family of MRD-codes. In this paper, we provide bounds on the list size of rank-metric codes containing generalized Gabidulin codes in order to determine whether or not a polynomial-time list decoding algorithm exists. We detect several families of rank-metric codes containing a generalized Gabidulin code as subcode which cannot be efficiently list decoded for any radius large enough and families of rank-metric codes which cannot be efficiently list…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Advanced Wireless Communication Techniques
