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Optimal Locally Repairable Codes: An Improved Bound and Constructions.
- Source :
- IEEE Transactions on Information Theory; Aug2022, Vol. 68 Issue 8, p5060-5074, 15p
- Publication Year :
- 2022
-
Abstract
- We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal. [ABSTRACT FROM AUTHOR]
- Subjects :
- HAMMING distance
LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157958015
- Full Text :
- https://doi.org/10.1109/TIT.2022.3161613