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 $\la S \setminus \{s,s^{-1}\} \ra \ne G$. In this paper we obtain the complete classification of distance-regular Cayley graphs $\cay(G;S)$ for such pairs of $G$ and $S$.