In this paper, we introduce two-level hierarchical locally repairable array codes (H-LRACs), a new class of codes designed to improve storage efficiency and fault tolerance in distributed storage systems. Firstly, we leverage the strengths of locally repairable codes (LRCs) and array codes to construct optimal \(\varvec{(r,\delta )}\) -LRACs with long code lengths. Then we introduce the concept of array codes with hierarchical locality, which offer a higher level of data protection through a multi-level locality structure. A key contribution of this paper is that we derive a universal upper bound on the minimum distance of H-LRACs using an entropy-based approach. This bound is shown to be tight through the explicit constructions for H-LRACs, capitalizing on optimal \(\varvec{(r,\delta )}\) -LRAC constructions. Finally, we extend the bound to LRACs with an arbitrary level of hierarchical locality.
