On distance-regular Cayley graphs of generalized dicyclic groups

Let $G$ be a generalized dicyclic group with identity $1$. An inverse closed subset $S$ of $G\setminus \{1\}$ is called minimal if $⟨S⟩=G$ and there exists some $s\in S$ such that $\langle S\setminus{s,s^{-1}} \rangle\neq G$\mathrm{.}Inthispaper,wecharacterizedistance-regularCayleygraphs$$\mathrm{C}\mathrm{a}\mathrm{y}$(G,S)$of$G$undertheconditionthat$S$ is minimal.