Certain strongly regular Cayley graphs on 𝔽22(2s+1) from cyclotomy

We give a construction of negative Latin square type strongly regular Cayley graphs on F"2"^"2"^"("^"2"^"s"^"+"^"1"^") with parameters (2^2^(^2^s^+^1^),2(2^2^s-1)(2^2^s^+^1+1)/3,4(2^2^s-1)^2/9-2,2(2^2^s^+^1+1)(2^2^s-1)/9) for every s>=1 based on choosing suitable cyclotomic classes on F"2"^"2"^"("^"2"^"s"^"+"^"1"^") and the computation of certain Gauss sums.

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