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Designs, Codes and Cryptography

, Volume 72, Issue 1, pp 53–75 | Cite as

Coset intersection of irreducible plane cubics

  • Gábor Korchmáros
  • Nicola PaceEmail author
Article
  • 187 Downloads

Abstract

In a projective plane \(PG(2,\mathbb K )\) over an algebraically closed field \(\mathbb K \) of characteristic \(p\ge 0\), let \(\Omega \) be a pointset of size \(n\) with \(5\le n \le 9\). The coset intersection problem relative to \(\Omega \) is to determine the family \(\mathbf F\) of irreducible cubics in \(PG(2,\mathbb K )\) for which \(\Omega \) is a common coset of a subgroup of the additive group \((\mathcal F ,+)\) for every \(\mathcal F \in \mathbf F\). In this paper, a complete solution of this problem is given.

Keywords

Plane cubic curves Abelian group Coset Configuration Projective plane 

Mathematics Subject Classification

14H52 05B30 

Notes

Acknowledgments

Nicola Pace is supported by FAPESP (Fundação de Amparo a Pesquisa do Estado de São Paulo), procs no. 12/03526-0.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità della BasilicataPotenzaItaly
  2. 2.Inst. de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil

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