1,721,020 research outputs found
On Singer action on Hermitian varieties
No full textWe show that a non-degenerate Hermitian variety H(2n, q2) in PG(2n, q2) can be partitioned in Baer parabolic quadrics Q(2n, q), if q is odd, or in Baer symplectic spaces W(2n−1, q), if q is even.We construct a partial spread of H(4, q2) of size (q5+1)/(q+1), admitting a group of order (q5+1)/(q+1) and a hyperoval of size 2(q5+1)/(q+1) on DH(4, q2), the point line dual generalized quadrangle of H(4, q2), admitting a dihedral group of order 2(q5 + 1)/(q + 1)
Hyperovals on H (3, q2) left invariant by a group of order 6 (q+1)3
No full textThree new infinite families of hyperovals on the generalized quadrangle H(3,q2) (q=ph, p a prime) of sizes 6(q+1), 12(q+1) 2 (if q>7) and 6(q+1)2 (if p>3) are constructed. Furthermore they turn out to be invariant under the action of a linear collineation group of order 6(q+1)3 that fixes no point or line in a secant plane of H(3,q2). In particular the hyperovals of size 6(q+1)2 are transitive. © 2013 Elsevier B.V. All rights reserved
Geometric constructions of two-character sets
No full textA two-character set in a finite projective space is a set of points with the property that the intersection number with any hyperplanes only takes two values. In this paper constructions of some two-character sets are given. In particular, infinite families of tight sets of the symplectic generalized quadrangle W(3,q2) and the Hermitian surface H(3,q2) are provided. A quasi-Hermitian variety H in PG(r,q2) is a combinatorial generalization of the (non-degenerate) Hermitian variety H(r,q2) so that H and H(r,q2) have the same number of points and the same intersection numbers with hyperplanes. Here we construct two families of quasi-Hermitian varieties, for r,q both odd, admitting PΓO+ (r+1,q) and PΓO- (r+1,q) as automorphisms group
On q–covering designs
Full text linkA q–covering design Cq (n, k, r), k ≥ r, is a collection X of (k − 1)–spaces of PG(n − 1, q) such that every (r − 1)–space of PG(n − 1, q) is contained in at least one element of X. Let Cq (n, k, r) denote the minimum number of (k −1)–spaces in a q–covering design Cq (n, k, r). In this paper improved upper bounds on Cq (2n, 3, 2), n ≥ 4, Cq (3n + 8, 4, 2), n ≥ 0, and Cq (2n, 4, 3), n ≥ 4, are presented. The results are achieved by constructing the related q–covering designs
On subspace codes
Full text linkIt is shown that any projective bundle of (Formula presented.) gives rise to a (Formula presented.) subspace code
On (0, α) -sets of generalized quadrangles
No full textSeveral infinite families of (0,α)-sets, α≥1, of finite classical and non-classical generalized quadrangles are constructed. When α=1 a (0,α)-set of a generalized quadrangle is a partial ovoid. We construct a maximal partial ovoid of H(4,q2), for any q, of size 2q3+q2+1, which generalizes the unique largest partial ovoid of H(4,4) of size 21 found in [11], and a maximal partial ovoid of Q-(5,q) of size (q+1)2, for any q. A tight set of a GQ(q-1,q+1) is also provided. © 2014 Elsevier Inc
Affine vector space partitions and spreads of quadrics
No full textAn affine spread is a set of subspaces of AG(n,q) of the same dimension that partitions the points of AG(n,q). Equivalently, an affine spread is a set of projective subspaces of PG(n,q) of the same dimension which partitions the points of PG(n,q)\H∞; here H∞ denotes the hyperplane at infinity of the projective closure of AG(n,q). Let Q be a non-degenerate quadric of H∞ and let Π be a generator of Q, where Π is a t-dimensional projective subspace. An affine spread P consisting of (t+1)-dimensional projective subspaces of PG(n,q) is called hyperbolic, parabolic or elliptic (according as Q is hyperbolic, parabolic or elliptic) if the following hold: Each member of P meets H∞ in a distinct generator of Q disjoint from Π; Elements of P have at most one point in common; If S,T∈P, |S∩T|=1, then ⟨S,T⟩∩Q is a hyperbolic quadric of Q. In this note it is shown that a hyperbolic, parabolic or elliptic affine spread of PG(n,q) is equivalent to a spread of Q+(n+1,q), Q(n+1,q) or Q-(n+1,q), respectively
Sets of even type on H (5, q 2), q even
No full textA construction of a set of type (0,2,q,q2-q) with respect to subgenerators of H(5,q2), q even, is given, generalizing the 126-hyperoval of H(5,4)
Intriguing sets of W(5,q), q even
No full textInfinite families of (q + 1)-ovoids and (q2 + 1)-tight sets of the symplectic polar space W(5,q), q even, are constructed. The (q + 1)-ovoids arise from relative hemisystems of the Hermitian surface H(3,q2) and from certain orbits of the Suzuki group Sz(q) in his projective 4-dimensional representation. The tight sets are closely related to the geometry of an ovoid of W(3,q). Other constructions of sporadic intriguing sets are also given. © 2014
A note on equidistant subspace codes
No full textEquidistant subspace codes are studied. A classification of the largest 1-intersecting codes in PG(5,2), whose codewords are planes, is provided. Also, new constructions of large equidistant codes are presented
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