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Constructions of MDS, Near MDS and Almost MDS Codes From Cyclic Subgroups of F* q 2.
- Source :
- IEEE Transactions on Information Theory; Dec2022, Vol. 68 Issue 12, p7817-7831, 15p
- Publication Year :
- 2022
-
Abstract
- Linear codes achieving or nearly achieving the Singleton bound are interesting in both theory and practice. The objective of this paper is to construct several infinite families of MDS, near MDS and almost MDS codes from some special cyclic subgroups of ${\mathbb {F}}_{q^{2}}^{*}$. To this end, the augmentation and extension techniques are used. The codes in this paper have flexible parameters and their lengths could be large. The minimum linear locality of the codes constructed in this paper is also studied. Some infinite families of optimal linearly locally recoverable codes are obtained. Besides, some codes in this paper are proved to be proper for error detection. [ABSTRACT FROM AUTHOR]
- Subjects :
- CYCLIC codes
LINEAR codes
CYCLIC loads
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 :
- 160651301
- Full Text :
- https://doi.org/10.1109/TIT.2022.3194914