On distance-regular Cayley graphs on abelian groups

Let $G$ denote a finite abelian group with identity 1 and let $S$ denote an inverse-closed subset of $G\setminus 1$, which generates $G$ and for which there exists $s\in S$, such that $\text{la}S\setminus \{s,s^{-1}\}\text{ra}\mathrm{\ne }G$. In this paper we obtain the complete classification of distance-regular Cayley graphs $\text{cay}(G;S)$ for such pairs of $G$ and $S$.