Two results are proved: (1) In PG(3, q), q=2 h, h>~3, every q3-arc can be uniquely completed to a (q + 1)3-arc. (2) In PG(4, q), q = 2", h ~> 3, every (q + 1)4-arc is a normal rational curve. ## 1. In~oduction We assume throughout this paper that the base field GF(q) is of order q = 2 h, where h i
The Uniqueness of the 1-System of Q−(7, q), q Odd
✍ Scribed by D. Luyckx; J.A. Thas
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 348 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0097-3165
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In this paper we prove that the projections along reguli of a translation spread of the classical generalized hexagon H (q) are translation ovoids of Q(4, q). As translation ovoids of Q(4, 2 r ) are elliptic quadrics, this forces that all translation spreads of H (2 r ) are semi-classical. By repres
## Abstract The existence of a (__q,k__, 1) difference family in __GF__(__q__) has been completely solved for __k__ = 3,4,5,6. For __k__ = 7 only partial results have been given. In this article, we continue the investigation and use Weil's theorem on character sums to show that the necessary condi