A Family of Gauss Type Hadamard Difference Sets

A Hadamard difference set (HDS) $D$ of order $u^2$ in an abelian group $G$ satisfies $|χ(D)|=u$ for every nontrivial character $χ$ of $G$. We call such a character value naive if it is divisible by $u$, i.e., if it is equal to $u$ times a root of unity. All previously known abelian HDSs only have na