Non-GRS type MDS and AMDS codes from extended TGRS codes
Meiying Zhang, Shudi Yang, Yanbin Zheng
TL;DR
This paper constructs new classes of extended TGRS codes that are MDS or AMDS, not equivalent to GRS codes, and analyzes their properties including covering radii and deep holes.
Contribution
It introduces a novel class of extended TGRS codes with specific MDS and AMDS properties, expanding the understanding of code equivalence and error correction.
Findings
Constructed extended TGRS codes that are MDS or AMDS.
Proved these codes are not equivalent to GRS codes.
Computed covering radii and deep holes for these codes.
Abstract
Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent error-correcting capabilities. In this paper, we construct a class of extended twisted generalized Reed-Solomon (TGRS) codes and determine the necessary and sufficient conditions for these codes to be MDS or AMDS. Additionally, we prove that these codes are not equivalent to generalized Reed-Solomon (GRS) codes. As an application, under certain circumstances, we compute the covering radii and deep holes of these codes.
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