In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes \(\mathcal {C}_{\varvec{\alpha , t, h, \eta }}\) with twists \(\varvec{t} = (1, 2)\) and hooks \(\varvec{h} = (0, 1)\) over the finite field \(\mathbb {F}_q\), providing a non-trivial example over \(\mathbb {F}_{16}\) and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull.

在本文中，我们找到了多重扭曲Reed-Solomon码是MDS的充要条件。特别地，我们引入了一类新的 MDS 双扭曲 Reed-Solomon 码\(\mathcal {C}_{\varvec{\alpha , t, h, \eta }}\)，其扭曲\(\varvec{t } = (1, 2)\)并在有限域\(\mathbb {F}_q\ ) 上挂钩\(\varvec{h} = (0, 1)\)，提供了一个关于\(的重要示例\mathbb {F}_{16}\)和大小最大为 17 的有限域的枚举。此外，我们获得了小维包的多扭曲 Reed-Solomon 码存在的必要条件。因此，我们推导了小维包 MDS 多扭曲 Reed-Solomon 码存在的条件。