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O'Keefe, Christine M.; Thas, J. A.

doi:10.1023/a:1008677211380

Journal of Algebraic Combinatorics

1997

DOI: 10.1023/a:1008677211380

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Christine M. O'Keefe

J. A. Thas

Abstract: Abstract.We generalise the definition and many properties of flocks of quadratic cones in PG(3, q) to partial flocks of quadratic cones with vertex a point in PG(n, q), for n ≥ 3 odd.

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Cited by 4 publications

References 11 publications

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Configurations of ovals

Penttila¹

2003

J.Geom.

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We survey the known hyperovals in PG(2, q). We then survey the relationship of the study of configurations of ovals in PG(2, q) called augmented fans to that of ovoids of PG(3, q), flocks of the quadratic cone of PG(3, q), flocks of a translation oval cone of PG(3, q) and spreads of certain generalised quadrangles of order q. We also consider the configurations of ovals in PG(2, q) called herds and their relationship with flocks of the quadratic cone of PG(3, q).

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Configurations of ovals

Penttila¹

2003

J.Geom.

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Flocks and partial flocks of quadrics: a survey

Thas

2001

Journal of Statistical Planning and Inference

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Some remarks on flocks

Bader¹,

O'Keefe

Penttila³

2004

J. Aust. Math. Soc.

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New proofs are given of the fundamental results of Bader, Lunardon and Thas relating flocks of the quadratic cone in PG(3, q), q odd, and BLT-sets of Q(4, q). We also show that there is a unique BLT-set of H(3, 9). The model of Penttila for Q(4, q), q odd, is extended to Q(2m, q) to construct partial flocks of size qm/2 + m/2 -1 of the cone Jt in PG(2m -1, q) with vertex a point and base Q(2m -2,q), where q is congruent to 1 or 3 modulo 8 and m is even. These partial flocks are larger than the largest previously known for m > 2. Also, the example of O'Keefe and Thas of a partial flock of Jf in PG(5, 3) of size 6 is generalised to a partial flock of the cone Jt? of PG(2pn -1, p) of size 2pn, for any prime p congruent to 1 or 3 modulo 8, with the corresponding partial BLT-set of Q(2pn, p) admitting the symmetric group of degree 2pn + 1.2000 Mathematics subject classification: primary 51E12; secondary 51A40, 51A5O, 51E20, O5B25.

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Untitled

Abstract: Abstract.We generalise the definition and many properties of flocks of quadratic cones in PG(3, q) to partial flocks of quadratic cones with vertex a point in PG(n, q), for n ≥ 3 odd.

Cited by 4 publications

References 11 publications

Configurations of ovals

Configurations of ovals

Flocks and partial flocks of quadrics: a survey

Some remarks on flocks

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