New MDS codes of non-GRS type and NMDS codes

Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes.