MDS multi-twisted Reed-Solomon codes with small dimensional hull

Abstract 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 $$\varv...
Ausführliche Beschreibung

Abstract 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. Ausführliche Beschreibung