Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3, 32h+1)

Using a class of permutation polynomials of F32h+1 obtained from the Ree-Tits slice symplectic spreads in PG(3, 3(2h+1)), we construct a family of skew Hadamard difference sets in the additive group of F32h+ 1. With the help of a computer, we show that these skew Hadamard difference sets are new when h = 2 and h = 3. We conjecture that they are always new when It > 3. Furthermore, we present a variation of the classical construction of the twin prime power difference sets, and show that inequivalent skew Hadamard difference sets lead to inequivalent difference sets with twin prime power parameters. (c) 2006 Elsevier Inc. All rights reserved.