Inequivalence of skew Hadamard difference sets and triple intersection numbers modulo a prime

摘要

Recently, Feng and Xiang \cite{FX113} found a new construction of skewHadamard difference sets in elementary abelian groups. In this paper, weintroduce a new invariant for equivalence of skew Hadamard difference sets,namely triple intersection numbers modulo a prime, and discuss inequivalencebetween Feng-Xiang skew Hadamard difference sets and the Paley difference sets.As a consequence, we show that their construction produces infinitely many skewHadamard difference sets inequivalent to the Paley difference sets.