Symplectic spreads and permutation polynomials

Details Symplectic spreads and permutation polynomials Symplectic spreads and permutation polynomials

2008-10-16

arxiv.org/abs/0810.2839v1

Finite Fields and Applications, Springer Lecture Notes in Computer Science 2948 (2004), 79--88

Mathematics

Combinatorics

9 pages. This paper was published in 2004. I post it now for greater accessibility

Scientific paper

Every symplectic spread of PG(3,q), or equivalently every ovoid of Q(4,q), is shown to give rise to a certain family of permutation polynomials of GF(q) and conversely. This leads to an algebraic proof of the existence of the Tits-Luneburg spread of W(2^{2h+1}) and the Ree-Tits spread of W(3^{2h+1}), as well as to a new family of low-degree permutation polynomials over GF(3^{2h+1}). We prove the permutation property of the latter polynomials via an odd characteristic analogue of Dobbertin's approach to uniformly representable permutation polynomials over GF(2^n). These new permutation polynomials were later used by Ding, Wang, and Xiang in arXiv:math/0609586 to produce new skew Hadamard difference sets.

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