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Small Complete Caps from Singular Cubics |
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| Authors: | Nurdagül Anbar Daniele Bartoli Massimo Giulietti Irene Platoni |
| Institution: | 1. Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli‐Tuzla, Istanbul, Turkey;2. Dipartimento di Matematica e Informatica, University of Perugia, Perugia, Italy;3. Dipartimento di Matematica, University of Trento, Povo (TN), Italy |
| Abstract: | New families of complete caps in finite Galois spaces are obtained. For most pairs  with  and  , they turn out to be the smallest known complete caps in  . Our constructions rely on the bicovering properties of certain plane arcs contained in plane cubic curves with a cusp. |
| Keywords: | galois affine spaces bicovering arcs complete caps quasi‐perfect codes cubic curves MSC (2010): 51E20 |