A Multi Secret Image sharing scheme can share several secret images among certain participators securely. Boolean-based secret sharing schemes are one kind of secret sharing method with light-weighted computation compared to the previous complex algebraic-based methods, which can realize the sharing of multi secret images. However, the existing Boolean-based multi secret sharing schemes are mostly restricted to the particular case of (2, n) and (n, n), only few Boolean-based multi secret sharing schemes study the general access structure, and the shares are mostly meaningless. In this paper, a new Boolean-based multi secret sharing scheme with the general access structure is proposed. All the shares are meaningful, which can avoid attracting the attention of adversaries, and the secret images can be recovered in a lossless manner. The feasibility of the scheme is proven, the performance is validated by the experiments on the gray images, and the analysis of the comparison with other methods is also given out.

The erasure codes are widely used in the distributed storage with low redundancy compared to the replication method. However, the current research studies about the erasure codes mainly focus on the encoding methods, while there are few studies on the decoding methods. In this paper, a novel erasure decoding method is proposed; it is a general decoding method and can be used both over the multivariate finite field and the binary finite field. The decoding of the failures can be realized based on the transforming process of the decoding transformation matrix, and it is convenient to avoid the overburdened visiting problem by tiny modification of the method. The correctness of the method is proved by the theoretical analysis; the experiments about the comparison with the traditional methods show that the proposed method has better decoding efficiency and lower reconstruction bandwidth.

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.