Inequivalence of Skew Hadamard Difference Sets and Triple Intersection Numbers Modulo a Prime

Recently, Feng and Xiang [10] found a new construction of skew Hadamard difference sets in elementary abelian groups. In this paper, we introduce a new invariant for equivalence of skew Hadamard difference sets, namely triple intersection numbers modulo a prime, and discuss inequivalence between Feng-Xiang skew Hadamard difference sets and the Paley difference sets. As a consequence, we show that their construction produces infinitely many skew Hadamard difference sets inequivalent to the Paley difference sets.