Ovoids with a pencil of translation ovals

1996 ◽  
Vol 62 (1) ◽  
Author(s):  
ChristineM. O'Keefe ◽  
Tim Penttila
Keyword(s):  
Translation Ovals

Ovoids and Translation Ovals

1997 ◽  
Vol 56 (3) ◽  
pp. 607-624 ◽  
Author(s):  
Tim Penttila ◽  
Cheryl E. Praeger
Keyword(s):  
Translation Ovals

Pencils of translation ovals in translation planes

1994 ◽  
Vol 51 (2) ◽  
pp. 113-121 ◽  
Author(s):  
D. G. Glynn ◽  
G. F. Steinke
Keyword(s):  
Translation Planes ◽  
Translation Ovals

scholarly journals Translation Hyperovals and $\mathbb{F}_2$-Linear Sets of Pseudoregulus Type

10.37236/8818 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Jozefien D'haeseleer ◽  
Geertrui Van de Voorde
Keyword(s):  
Finite Fields ◽  
Point Sets ◽  
Linear Set ◽  
Linear Sets ◽  
Even Order ◽  
Translation Ovals

In this paper, we study translation hyperovals in PG(2,qk). The main result of this paper characterises the point sets defined by translation hyperovals in the André/Bruck-Bose representation. We show that the affine point sets of translation hyperovals in PG(2,qk) are precisely those that have a scattered F2-linear set of pseudoregulus type in PG(2k−1,q) as set of directions. This correspondence is used to generalise the results of Barwick and Jackson who provided a characterisation for translation hyperovals in PG(2,q2), see [S.G. Barwick, Wen-Ai Jackson, A characterization of translation ovals in finite even order planes. Finite fields Appl. 33 (2015), 37--52.].

Laguerre planes of even order and translation ovals

1994 ◽  
Vol 51 (2) ◽  
pp. 105-112 ◽  
Author(s):  
D. G. Glynn ◽  
G. F. Steinke
Keyword(s):  
Even Order ◽  
Laguerre Planes ◽  
Translation Ovals

scholarly journals A characterization of translation ovals in finite even order planes

2015 ◽  
Vol 33 ◽  
pp. 37-52 ◽  
Author(s):  
S.G. Barwick ◽  
Wen-Ai Jackson
Keyword(s):  
Even Order ◽  
Translation Ovals
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