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MDS, Near-MDS or 2-MDS Self-Dual Codes via Twisted Generalized Reed-Solomon Codes.
- Source :
- IEEE Transactions on Information Theory; Dec2022, Vol. 68 Issue 12, p7832-7841, 10p
- Publication Year :
- 2022
-
Abstract
- Twisted generalized Reed-Solomon (TGRS) codes are a family of codes that contains a large number of maximum distance separable (MDS) codes that are non-equivalent to generalized Reed-Solomon (GRS) codes. In this paper, we characterize a sufficient and necessary condition that a twisted Reed-Solomon (TRS) code with two twists is MDS; give a sufficient and necessary condition that a TGRS code with two twists is self-dual, and present some constructions of self-dual TGRS codes. These self-dual codes are MDS, NMDS or 2-MDS. Furthermore, we study the non-GRS properties of TGRS codes with two twists and prove that these codes are non-GRS in most cases. [ABSTRACT FROM AUTHOR]
- Subjects :
- REED-Solomon codes
REED-Muller codes
LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 160651282
- Full Text :
- https://doi.org/10.1109/TIT.2022.3190676