Unitals and Unitary Polarities in Symmetric Designs

@article{Mathon1997UnitalsAU,
  title={Unitals and Unitary Polarities in Symmetric Designs},
  author={Rudolf Mathon and Tran van Trung},
  journal={Des. Codes Cryptography},
  year={1997},
  volume={10},
  pages={237-250}
}
We extend the notion of unital as well as unitary polarity from finite projective planes to arbitrary symmetric designs. The existence of unitals in several families of symmetric designs has been proved. It is shown that if a unital in a point-hyperplane design PGd−1(d,q) exists, thend = 2 or 3; in particular, unitals and ovoids are equivalent in case d = 3. Moreover, unitals have been found in two designs having the same parameters as the PG4(5, 2), although the latter does not have a unital… CONTINUE READING

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