Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals

@inproceedings{Buratti2003SemiBooleanSQ,
  title={Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals},
  author={Marco Buratti and Alberto Del Fra},
  year={2003}
}
A dimensional dual hyperoval satisfying property (H) [6] in a projective space of order 2 is naturally associated with a ‘‘semi-Boolean’’ Steiner quadruple system. The only known examples are associated with Boolean systems. For every d > 2, we construct a new ddimensional dual hyperoval satisfying property (H) in PGðdðd þ 3Þ=2; 2Þ; its related semiBoolean system is the Teirlinck one. It is universal and admits quotients in PGðn; 2Þ, with 4d < n < dðd þ 3Þ=2, if dd 6. We also prove the… CONTINUE READING

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