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Constructions of Optimal Cyclic Codes With h-Level Hierarchical Locality
  • Xing Liu
Xing Liu

Corresponding Author:[email protected]

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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 study h-level H-LRCs where h is not limited to 2. We present four constructions of cyclic h-level H-LRCs with length ln1 such that gcd(lq) = 1 and n1|(q−1). These four classes of cyclic h-level H-LRCs are optimal with respect to the generalized Singleton-like bound. The minimum Hamming distances of them are d = δ1, δ1+1, δ1+2, δ1h respectively. Furthermore, these four classes of cyclic h-level H-LRCs have new and flexible parameters which are not covered in the literature. By setting the parameter l appropriately for the third construction, one can construct optimal cyclic h-level H-LRCs with length n|(q−1) and distance d = δ1+σ where σ is not limited to 0, 1, 2, δh.
23 Apr 2024Submitted to TechRxiv
29 Apr 2024Published in TechRxiv