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In this paper, generalizing the result in \cite{GXY}, we construct stronglyregular Cayley graphs by using union of cyclotomic classes of $\F_q$ and Gausssums of index $w$, where $w\geq 2$ is even. In particular, we obtain threeinfinite families of strongly regular graphs with new parameters.

Constructions of Strongly Regular Cayley Graphs using Even Index Gauss Sums