Geodesic
Translation hyperovals and \(\mathbb{F}_2\)-linear sets of pseudoregulus type
Jozefien D'haeseleer ; Geertrui Van de Voorde1
1University of Canterbury
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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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.].
DOI : 10.37236/8818
Classification : 51E21, 51E20
Mots-clés : translation hyperovals, André/Bruck-Bose representation, linear sets

Jozefien D'haeseleer    ; Geertrui Van de Voorde  1

1 University of Canterbury 
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     title = {Translation hyperovals and {\(\mathbb{F}_2\)-linear} sets of pseudoregulus type},
     journal = {The electronic journal of combinatorics},
     year = {2020},
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Jozefien D'haeseleer; Geertrui Van de Voorde. Translation hyperovals and \(\mathbb{F}_2\)-linear sets of pseudoregulus type. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8818

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