Constructions of Optimal Cyclic Codes With h -Level Hierarchical Locality
Xing Liu · IEEE Transactions on Information Theory · 2025
In order to correct different numbers of erasures in distributed storage systems, the design of locally repairable codes with hierarchical locality (H-LRCs) is crucial. In this paper, we studyh-level H-LRCs wherehis not limited to 2. We present six classes of cyclich-level H-LRCs which are optimal with respect to the generalized Singleton-like bound. The first five classes of cyclich-level H-LRCs have length$ln_{1}$such that$\gcd (l,q)=1$, and$n_{1}|(q-1)$or$n_{1}|(q+1)$. The last class of cyclich-level H-LRCs has length$n|(q+1)$. The minimum Hamming distances of them are$d=\delta _{1}+i$whereican take 0, 2,$\delta _{h}$, and so on. Furthermore, these six classes of cyclich-level H-LRCs have new parameters which are not covered in the literature.