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 $\mathcal{ C}_{ \bm \alpha, \bm t, \bm h, \bm \eta}$ with twists $\bm t = (1, 2)$ and hooks $\bm h = (0, 1)$ 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.
Categories: cs.IT cs.CR math.AC math.IT