A Class of Extended Generalized RDP Codes

In 2022, [1] proposed a new construction for binary array codes with three parity columns, which can deduce some types of maximum distance separable (MDS) array codes. It was left as an open problem generalizing this construction to support more parity columns. This paper considers such a generalization and reveals it as a class of extended generalized RDP codes. We present the relationship between new codes and codes over all-one polynomial rings. Furthermore, we explicitly provide two new MDS array codes, one designed for four parity columns. We also propose two corresponding approaches for quickly computing syndromes of the new codes, both of which reach the lowest known asymptotic complexities.