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.

翻译：最大距离可分（MDS）码与近最大距离可分（NMDS）码因其代数特性与优异的纠错能力，已被广泛应用于通信系统、数据存储和量子编码等多个领域。本文聚焦于一类特定的线性码，建立了其成为MDS码或NMDS码的充分必要条件。此外，我们采用经典的舒尔方法证明该类码与广义里德-所罗门码不等价。