Constructions of Non-Generalized Reed–Solomon MDS Codes

Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes that are MDS yet not generalized Reed-Solomon codes, called non-generalized Reed-Solomon MDS codes, started with the work by Roth and Lemple (1989), where the first examples were exhibited. It then gained traction thanks to the work by Beelen et al. (2017), wh