This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns to the generator matrix of original TGRS codes. Secondly, the necessary and sufficient conditions for these codes to be MDS or almost MDS (AMDS) codes are derived. Then, by analyzing the AMDS properties of their dual codes, the necessary and sufffcient conditions for them to be NMDS codes are established. Furthermore, some examples are given to verify the main results. Finally, we determine the non-generalized Reed-Solomon (non-GRS) characteristics of them via the Schur product method.

翻译：本文研究了扩展广义扭转Reed-Solomon（TGRS）码的最大距离可分（MDS）与近MDS（NMDS）性质。首先，通过在原始TGRS码的生成矩阵后附加三列，构造了一类扩展TGRS（ETGRS）码。其次，推导了这些码为MDS或几乎MDS（AMDS）码的充分必要条件。随后，通过分析其对偶码的AMDS性质，建立了其为NMDS码的充分必要条件。此外，给出若干实例以验证主要结论。最后，利用Schur乘积方法确定了这些码的非广义Reed-Solomon（non-GRS）特性。