Decoding algorithms for symbol-error correction in MDS array codes via superregular matrices

Abstract Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate decoding algorithms for MDS array codes over $$\mathbb {F}_q^b$$ F q b (viewed algebraically as the extension field $$\mathbb {F}_{q^b}$$ F q b ), using existing constructions based on superregular matrices, with particular emphasis on Vandermonde and Cauchy structures. We propose explicit decoding algorithms for MDS array codes with redundancy m , capable of correcting symbol errors without prior knowledge of their locations. The proposed framework applies to symbol-error patterns and relies on algebraic relations that are not immediate consequences of existing decoding methods. In particular, the algorithms correct one symbol error for $$m \ge 2$$ m ≥ 2 and two symbol errors for $$m \ge 4$$ m ≥ 4 . For the two-error case, the decoding procedure admits a simplified form when Vandermonde superregular matrices are employed, which significantly reduces the number of algebraic operations. We also analyze the algebraic structure of the three-symbol-error case when all errors occur in information symbols, thereby indicating possible extensions of the proposed approach to higher error-correction capability. The proposed decoding procedures involve structured algebraic operations over $$\mathbb {F}_q^b$$ F q b and the solution of small linear systems, making them suitable for moderate parameter sizes and practical implementations.