394 research outputs found
Transitive and Co-Transitive Caps
A cap in PG(r,q) is a set of points, no three of which are collinear. A cap
is said to be transitive if its automorphism group in PGammaL(r+1,q) acts
transtively on the cap, and co-transitive if the automorphism group acts
transtively on the cap's complement in PG(r,q). Transitive, co-transitive caps
are characterized as being one of: an elliptic quadric in PG(3,q); a
Suzuki-Tits ovoid in PG(3,q); a hyperoval in PG(2,4); a cap of size 11 in
PG(4,3); the complement of a hyperplane in PG(r,2); or a union of Singer orbits
in PG(r,q) whose automorphism group comes from a subgroup of GammaL(1,q^{r+1}).Comment: To appear in The Bulletin of the Belgian Mathematical Society - Simon
Stevi
Subspace code constructions
We improve on the lower bound of the maximum number of planes of mutually intersecting in at most one point leading to the following
lower bound: for
constant dimension subspace codes. We also construct two new non-equivalent
constant dimension subspace orbit-codes
On curves covered by the Hermitian curve
For each proper divisor d of (r^2-r+1), r being a power of a prime, maximal
curves over a finite field with r^2 elements covered by the Hermitian curve of
genus 1/2((r^2-r+1)/d-1) are constructed.Comment: 18 pages, Latex2
On Twisted Tensor Product Group Embeddings and the Spin Representation of Symplectic Groups: The Case q Odd
The group PSp8(q),  q odd, has a maximal subgroup isomorphic to 3.PSp2(q3) belonging to the Aschbacher class 𝒞9. It is the full stabilizer of a complete partial ovoid and of a complete partial 3-spread of 𝒲7(q)
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