On non-hyperelliptic flocks
L Bader, G Lunardon - European Journal of Combinatorics, 1994 - Elsevier
… The prove that a non-hyperelliptic flock of the quadratic cone, the associated translation
plane of which is either a semifield or a likeable plane, is isomorphic to one of the known …
plane of which is either a semifield or a likeable plane, is isomorphic to one of the known …
[HTML][HTML] On the classification of semifield flocks
A Blokhuis, M Lavrauw, S Ball - Advances in Mathematics, 2003 - Elsevier
… A flock F of K is a partition of K ⧹{v} into q n conics. If all the planes that contain a conic of the
flock share a line then the flock is called linear. Let v be the point … On non-hyperelliptic flocks …
flock share a line then the flock is called linear. Let v be the point … On non-hyperelliptic flocks …
On the sporadic semifield flock
I Cardinali, O Polverino, R Trombetti - Designs, Codes and Cryptography, 2003 - Springer
… When q is even, all semifield flocks are linear [8]. When q is odd, in … linear flocks, two infinite
classes of semifield flocks are known: the Kantor semifield flocks [14] and the Ganley flocks [7…
classes of semifield flocks are known: the Kantor semifield flocks [14] and the Ganley flocks [7…
A new semifield flock
L Bader, G Lunardon, I Pinneri - Journal of Combinatorial Theory, Series A, 1999 - Elsevier
… flock of K for which the planes of the q conics all contain a common point, is of the type just
described ([19]). The flock is called the Kantor semifield flock. … flock F( f, g) is a semifield flock if …
described ([19]). The flock is called the Kantor semifield flock. … flock F( f, g) is a semifield flock if …
Flocks, Ovoids of Q(4,q)and Designs
G Lunardon - Geometriae Dedicata, 1997 - Springer
… If F is a Kantor semifield flock (see [8]), then O(F) is the ovoid constructed in [… flocks produce
a new class of semifield ovoids (see [19]). In this paper we prove that if F is a semifield flock …
a new class of semifield ovoids (see [19]). In this paper we prove that if F is a semifield flock …
On monomial flocks
L Bader, D Ghinelli, T Penttila - European Journal of Combinatorics, 2001 - Elsevier
… monomial flocks of quadratic cones of PG(3, q), with emphasis on the case where the flock is
… In addition, we give a computer-free proof of the existence of the sporadic semifield flock of …
… In addition, we give a computer-free proof of the existence of the sporadic semifield flock of …
Symplectic spreads and permutation polynomials
… ■ When q is odd we can use Thas’ classification of flocks of the quadratic cone in PG(3,q) …
We realise that for many readers familiar with flocks and semifield flocks the next theorem is …
We realise that for many readers familiar with flocks and semifield flocks the next theorem is …
Searching for semifield flocks
I Pinneri - Discrete mathematics, 2002 - Elsevier
… The main result of this paper is: In PG(3,27) any semifield flock is isomorphic either to the
linear, Kantor–Knuth or Ganley flock. No new semifield or likeable flocks have been found. …
linear, Kantor–Knuth or Ganley flock. No new semifield or likeable flocks have been found. …
Translation ovoids
G Lunardon - Journal of Geometry, 2003 - Springer
… flocks and the classification theorem for such flocks due to L. Bader and the author (see [5]),
discussing a bound for the existence of sporadic semifield flocks … with a flock. Using the GF(s)…
discussing a bound for the existence of sporadic semifield flocks … with a flock. Using the GF(s)…
Commutative semifields of rank 2 over their middle nucleus
S Ball, M Lavrauw - Finite Fields with Applications to Coding Theory …, 2002 - Springer
… that contain conics of the flock the planes oj the flock. A flock F is equivalent to a flock F' if there
… cone that maps the planes of the flock F to the planes of the flock F'. If all the planes of the …
… cone that maps the planes of the flock F to the planes of the flock F'. If all the planes of the …