Geodesic
Ambient spaces of dimensional dual arcs
Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 5-23.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A $d$-dimensional dual arc in $PG( n, q)$ is a higher dimensional analogue of a dual arc in a projective plane. For every prime power $q$ other than 2, the existence of a $d$-dimensional dual arc ( $dge$ 2) in $PG( n, q)$ of a certain size implies $nled( d + 3)/2$ (Theorem 1). This is best possible, because of the recent construction of $d$-dimensional dual arcs in PG( d( d + 3)/2, $q)$ of size $sum^{ d-1} _{ i=0} q ^{i}$, using the Veronesean, observed first by Thas and van Maldeghem (Proposition 7). Another construction using caps is given as well (Proposition 10).
Keywords: dual arc, dual hyperoval, Veronesean 
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Yoshiara, Satoshi. Ambient spaces of dimensional dual arcs. Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 5-23. http://geodesic.mathdoc.fr/item/JAC_2004__19_1_a4/