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Small complete caps from nodal cubics
- Publication Year :
- 2013
-
Abstract
- Bicovering arcs in Galois affine planes of odd order are a powerful tool for constructing complete caps in spaces of higher dimensions. In this paper we investigate whether some arcs contained in nodal cubic curves are bicovering. For $m_1$, $m_2$ coprime divisors of $q-1$, bicovering arcs in $AG(2,q)$ of size $k\le (q-1)\frac{m_1+m_2}{m_1m_2}$ are obtained, provided that $(m_1m_2,6)=1$ and $m_1m_2<\sqrt[4]{q}/3.5$. Such arcs produce complete caps of size $kq^{(N-2)/2}$ in affine spaces of dimension $N\equiv 0 \pmod 4$. For infinitely many $q$'s these caps are the smallest known complete caps in $AG(N,q)$, $N \equiv 0 \pmod 4$.
- Subjects :
- Mathematics - Combinatorics
51E20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1305.3019
- Document Type :
- Working Paper