We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs in finite projective spaces, we give a new characterization of o-monomials.
@article{arxiv.2506.04080,
title = {Some constructions of non-generalized Reed-Solomon MDS Codes},
author = {Kanat Abdukhalikov and Cunsheng Ding and Gyanendra K. Verma},
journal= {arXiv preprint arXiv:2506.04080},
year = {2025}
}