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In this paper, we give a construction of strongly regular Cayley graphs onthe additive groups of finite fields based on three-valued Gauss periods. Asconsequences, we obtain two infinite families and one sporadic example of newstrongly regular Cayley graphs. This construction can be viewed as ageneralization of that of strongly regular Cayley graphs obtained in\cite{BLMX}.

Construction of strongly regular Cayley graphs based on three-valued Gauss periods