- in
hyperovals, a
description of the (known)
hyperovals implicitly gives all (known) ovals. The
ovals obtained by
removing a
point from a
hyperoval are...
- a
hyperoval or (n + 2)-arc. (A
finite oval is an (n + 1)-arc.) One
easily checks the
following essential property of a
hyperoval: For a
hyperoval Ω and...
-
various structures that are
contained in them. In particular, arcs, ovals,
hyperovals, unitals,
blocking sets, ovoids, caps,
spreads and all
finite analogues...
-
conjugacy classes. The
subgroups respectively have
orbits of 6,
called hyperovals, and
orbits of 7,
called Fano subplanes.
These sets
allow creation of...
- and acts
transitively on its
hyperovals (sets of 6
points such that no
three are on a line). The
subgroup fixing a
hyperoval is a copy of the alternating...
- at most qd + d − q. When
equality occurs, one
calls A a
maximal arc.
Hyperovals are
maximal arcs.
Complete arcs need not be
maximal arcs.
Normal rational...
-
discussed O'Keefe's work in
finite geometry, such as the
discovery of new
hyperovals, it
included a
paragraph on her
research using geometry in
secret sharing...
- = Dih(7) 36 = 1+14+21
Pairs of
points in P1(8) L3(4) A6 56 = 1+10+45
Hyperovals in P2(4);
three classes L4(3) PSp4(3):2 117 = 1+36+80
Symplectic polarities...
- to each
other if and only if q {\displaystyle q} is even. Let O be a
hyperoval in P G ( 2 , q ) {\displaystyle PG(2,q)} with q an even
prime power, and...
- d
divides q. In the
special case of d = 2,
maximal arcs are
known as
hyperovals which can only
exist if q is even. An arc K
having one
fewer point than...
