Optimal Cyclic (r, δ) Locally Repairable Codes With r + δ - 1 = (q+1)/4
Xing Liu, Qi Wen Zeng, Yao Hao, Yue Zhao, Jun Bo Zhong, Limengnan Zhou · 2021
Locally repairable codes (LRCs), due to the local erasure-correcting property, have been widely used in distributed storage systems. In this paper, we construct cyclic (r, δ) LRCs ((r, δ) CLRCs) which are optimal according to the Singleton-like bound. The locality of the new CLRCs satisfies that $r + \delta - 1 = \frac{{q + 1}}{4}$. This is different from those of CLRCs obtained by Qian and Zhang in 2020 which are $r + \delta - 1 = q + 1{\text{ and }}r + \delta - 1 = \frac{{q + 1}}{2}$. Then the parameters of our CLRCs are new.