Optimal Cyclic (r, δ) Locally Repairable Codes With r + δ - 1 = (q+1)/4

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 ...