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Computer Science > Information Theory

arXiv:2207.05479 (cs)
[Submitted on 12 Jul 2022]

Title:Bounds and Constructions of Singleton-Optimal Locally Repairable Codes with Small Localities

Authors:Weijun Fang, Bin Chen, Shu-Tao Xia, Fang-Wei Fu
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Abstract:Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum distance $d=6$, locality $r=3$ and minimum distance $d=7$ and locality $r=2$, respectively. Firstly, we establish equivalent connections between the existence of these two families of LRCs and the existence of some subsets of lines in the projective space with certain properties. Then, we employ the line-point incidence matrix and Johnson bounds for constant weight codes to derive new improved bounds on the code length, which are tighter than known results. Finally, by using some techniques of finite field and finite geometry, we give some new constructions of Singleton-optimal LRCs, which have larger length than previous ones.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2207.05479 [cs.IT]
  (or arXiv:2207.05479v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2207.05479

Submission history

From: Weijun Fang [view email]
[v1] Tue, 12 Jul 2022 11:45:10 UTC (244 KB)
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