On deep-holes of Gabidulin codes
Weijun Fang, Li-Ping Wang, and Daqing Wan
TL;DR
This paper investigates the properties of deep holes in Gabidulin codes, providing new insights into their covering radius, classification of deep holes, and criteria for identifying non-deep holes in both rank and Hamming metrics.
Contribution
It introduces the determination of the covering radius, classifies a class of deep holes, and establishes a criterion for identifying non-deep holes in Gabidulin codes.
Findings
Determined the covering radius of Gabidulin codes.
Identified a class of deep holes for Gabidulin codes.
Provided a necessary and sufficient condition for non-deep holes.
Abstract
In this paper, we determine the covering radius and a class of deep holes for Gabidulin codes with both rank metric and Hamming metric. Moreover, we give a necessary and sufficient condition for deciding whether a word is not a deep hole for Gabidulin codes, by which we study the error distance of a special class of words to certain Gabidulin codes.
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