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On 2 – (n 2, 2n, 2n–1) designs with three intersection numbers

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Abstract

The simple incidence structure \({\mathcal{D}(\mathcal{A},2)}\) , formed by the points and the unordered pairs of distinct parallel lines of a finite affine plane \({\mathcal{A}=(\mathcal{P}, \mathcal{L})}\) of order n > 4, is a 2 – (n 2,2n,2n–1) design with intersection numbers 0,4,n. In this paper, we show that the converse is true, when n ≥ 5 is an odd integer.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici, University of Palevmo, Viale delle Scienze, Ed. 8, I–90128, Palermo, Italy

    Andrea Caggegi & Giovanni Falcone

Authors
  1. Andrea Caggegi
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  2. Giovanni Falcone
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Corresponding author

Correspondence to Giovanni Falcone.

Additional information

Communicated by M. J. de Resmini.

Supported by M.I.U.R., Università di Palermo.

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Caggegi, A., Falcone, G. On 2 – (n 2, 2n, 2n–1) designs with three intersection numbers. Des Codes Crypt 43, 33–40 (2007). https://doi.org/10.1007/s10623-007-9051-z

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  • DOI: https://doi.org/10.1007/s10623-007-9051-z

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