Symplectic spreads and permutation polynomials
| dc.creator | Ball, Simeon | |
| dc.creator | Zieve, Michael E. | |
| dc.date | 2008-10-16 | |
| dc.date.accessioned | 2026-07-07T10:10:36Z | |
| dc.date.available | 2026-07-07T10:10:36Z | |
| dc.description | 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. | |
| dc.description | 9 pages. This paper was published in 2004. I post it now for greater accessibility | |
| dc.identifier | https://arxiv.org/abs/0810.2839 | |
| dc.identifier | http://arxiv.org/abs/0810.2839 | |
| dc.identifier | Finite Fields and Applications, Springer Lecture Notes in Computer Science 2948 (2004), 79--88 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171641 | |
| dc.subject | Combinatorics | |
| dc.subject | 51E23; 05B25, 11T06 | |
| dc.title | Symplectic spreads and permutation polynomials | |
| dc.type | text |