Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3,3^2h+1)

2006/09/21 by Cunsheng Ding, Ding, Cunsheng, Zeying Wang +3 · 1 citation
Computer Science · Engineering · Mathematics · #05B10 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B10

paper · pdf · doi:10.48550/arxiv.math/0609586

18 pages

arxiv created 2006/09/21 · openalex publication_date 2006/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a class of permutation polynomials of F_3^2h+1 obtained from the Ree-Tits symplectic spreads in PG(3,3^2h+1), we construct a family of skew Hadamard difference sets in the additive group of F_3^2h+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 h>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.

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• Symplectic spreads and permutation polynomials

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