A framework constructs new non-GRS MDS-NMDS codes from deep holes, yielding three new families while recovering prior results with lower computational complexity.
Non-GRS type MDS and AMDS codes from extended TGRS codes
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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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cs.IT 2years
2026 2verdicts
UNVERDICTED 2roles
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Extended TGRS codes are built by adding three columns to TGRS generator matrices; conditions for MDS/AMDS/NMDS are derived and non-GRS nature is shown via Schur product.
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A framework for constructing non-GRS MDS-NMDS codes from deep holes and its application
A framework constructs new non-GRS MDS-NMDS codes from deep holes, yielding three new families while recovering prior results with lower computational complexity.
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MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes
Extended TGRS codes are built by adding three columns to TGRS generator matrices; conditions for MDS/AMDS/NMDS are derived and non-GRS nature is shown via Schur product.