Skip to main content
Log in

On standard two-intersection sets in PG(rq)

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

In this paper, we extend and analyze in a finite projective space of any dimension the notion of standard two-intersection sets previously introduced in the projective plane by Penttila and Royle (Des Codes Cryptogr 6:229–245, 1995), see also Blokhuis and Lavrauw (J Combin Theory Ser A 99:377–382, 2002). Moreover, given a pair of suitable distinct standard two-intersection sets in a finite projective space it is possible to get further standard two-intersection sets by applying elementary set-theoretical operations to the elements of the pair.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blokhuis, A., Lavrauw, M.: On two-intersection sets with respect to hyperplanes in projective spaces. J. Combin. Theory Ser. A 99, 377–382 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cossidente, A., Durante, N., Marino, G., Penttila, T., Siciliano, A.: The geometry of some two-character sets. Des. Codes Cryptogr. 46, 231–241 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. De Finis, M.: On \(k\)-sets in \(PG(r, q)\), \(r\ge 3\). Rend. Mat. 3, 447–454 (1983)

  4. De Finis, M.: On \(k\)-sets of type \((m, n)\) in \(PG(3, q)\) with respect to planes. ARS Combin. 21, 119–136 (1986)

  5. Hamilton, N., Penttila, T.: Sets of type \((a, b)\) from subgroups of \(\Gamma L(1, p^R)\). J. Algebr. Combin. 13, 67–76 (2001)

  6. Lane-Harvard, L., Penttila, T.: Some strongly regular graphs with the parameters of Paley graphs. Australas. J. Combin. 61, 138–141 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Penttila, T., Royle, G.F.: Sets of type \((m, n)\) in the affine and projective planes of order nine. Des. Codes Cryptogr. 6, 229–245 (1995)

  8. Scafati, M.T.: Sui \(k\)-insiemi di uno spazio di Galois \(S_{r,q}\) a due soli caratteri nella dimensione \(d\). Rend. Accad. Naz. Lincei 60(8), 782–788 (1976)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fulvio Zuanni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zuanni, F. On standard two-intersection sets in PG(rq). J. Geom. 109, 26 (2018). https://doi.org/10.1007/s00022-018-0432-4

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00022-018-0432-4

Mathematics Subject Classification

Keywords

Navigation