A low-overhead repair code based on hybrid grouping

Reed–Solomon (RS) codes are widely adopted in large-scale distributed storage systems due to their optimal storage efficiency. However, repairing failed nodes in RS-based environments often requires intensive matrix inversions, which increase computational costs and extend recovery latency. This limitation becomes a critical bottleneck during multi-node failures. To address this challenge, we propose the Layered Elastic Non-Inverse Reconstruction Code (LENRC), a novel group-based repair scheme that integrates hybrid parity checks with polynomial reconstruction. LENRC eliminates the need for matrix inversion by employing a recursive polynomial method to directly establish linear relationships between failed and surviving blocks over finite fields, thereby significantly reducing decoding complexity. The scheme integrates global parity, intra-group parity, and Enhanced Interpolation Checks (ENIC) into a tiered architecture that adaptively selects repair paths based on failure patterns. Experimental results demonstrate that LENRC outperforms classic RS codes and state-of-the-art group repair codes, including RGRC, TLRC, SLRC, and CSLRC. Specifically, LENRC reduces single-node repair overhead by 8.7%–65.5% and shortens multi-node repair time by 4.4%–49.8%, while incurring only marginal storage overhead. These results highlight LENRC’s superior balance of storage efficiency, repair cost, and fault tolerance, representing a significant advancement for modern storage infrastructures.