New Classes of Optimal Cyclic Codes With Hierarchical Locality
Xing Liu, Qi Wen Zeng · IEEE Transactions on Information Theory · 2024
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 construct three classes of optimal cyclic H-LRCs. The minimum Hamming distance of the first class of optimal cyclic H-LRCs is$d=\delta _{1}=\delta +\mu n'+ u +1$while that of the second class of optimal cyclic H-LRCs is$d=\delta _{1}+1=\delta +\mu n'+ u +2$for some flexible integers$\delta,\mu, u $. The first two classes of optimal cyclic H-LRCs also have unbounded length. Although the length of the third class of optimal cyclic H-LRCs is not unbounded, it can reach large values. These classes of optimal cyclic H-LRCs by our constructions have new and flexible parameters compared with those in the literature.