On 2 – (n2, 2n, 2n–1) designs with three intersection numbers

  • Authors:

  • Andrea Caggegi;Giovanni Falcone

  • Affiliations:

  • Dipartimento di Metodi e Modelli Matematici, University of Palevmo, Palermo, Italy I---90128;Dipartimento di Metodi e Modelli Matematici, University of Palevmo, Palermo, Italy I---90128

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2007

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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 驴 5 is an odd integer.