Covering Radii and Deep Holes of Two Classes of Extended Twisted GRS Codes and Their Applications

Abstract

Maximum distance separable (MDS) codes that are not monomially equivalent to generalized Reed-Solomon (GRS) codes are called non-GRS MDS codes, which have important applications in communication and cryptography. Covering radii and deep holes of linear codes are closely related to their decoding problems. In the literature, the covering radii and deep holes of GRS codes have been extensively studied, while little is known about non-GRS MDS codes. In this paper, we study two classes of extended twisted generalized Reed-Solomon (ETGRS) codes involving their non-GRS MDS properties, covering radii, and deep holes. In other words, we obtain two classes of non-GRS MDS codes with known covering radii and deep holes. As applications, we further directly derive more non-GRS MDS codes, and get some results on the existence of their error-correcting pairs. As a byproduct, we find some connections between the well-known Roth-Lempel codes and these two classes ETGRS codes.