Designs, Codes and Cryptography

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

Coset intersection of irreducible plane cubics

  • Gábor Korchmáros
  • Nicola PaceEmail author


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.


Plane cubic curves Abelian group Coset Configuration Projective plane 

Mathematics Subject Classification

14H52 05B30 



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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