New families of complete caps in finite Galois spaces are obtained. For most pairs $(N,p^h)$ with $h>8$ and $N\equiv 0 \pmod 4$, they turn out to be the smallest known complete caps in $AG(N,p^h)$. Our constructions rely on the bicovering properties of certain plane arcs contained in plane cubic curves with a cusp.
Small Complete Caps from Singular Cubics
BARTOLI, DANIELE;GIULIETTI, Massimo;
2014
Abstract
New families of complete caps in finite Galois spaces are obtained. For most pairs $(N,p^h)$ with $h>8$ and $N\equiv 0 \pmod 4$, they turn out to be the smallest known complete caps in $AG(N,p^h)$. Our constructions rely on the bicovering properties of certain plane arcs contained in plane cubic curves with a cusp.File in questo prodotto:
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