1,721,074 research outputs found
The m-ovoids of W(5,2) and their generalizations
No full textIn this paper we are concerned with m-ovoids of the symplectic polar space W(2n+1,q), q even. In particular we show the existence of an elliptic quadric of PG(2n+1,q) not polarizing to W(2n+1,q) forming a [Formula presented]-ovoid of W(2n+1,q). A further class of (q+1)-ovoids of W(5,q) is exhibited. It arises by gluing together two orbits of a subgroup of PSp(6,q) isomorphic to PSL(2,q2). We also show that the obtained m-ovoids do not fall in any of the examples known so far in the literature. Moreover, a computer classification of the m-ovoids of W(5,2) is acquired. It turns out that W(5,2) has m-ovoids if and only if m=3 and that there are exactly three pairwise non-isomorphic examples. The first example comes from an elliptic quadric Q−(5,2) polarizing to W(5,2), whereas the other two are the 3-ovoids previously mentioned
An infinite family of m-ovoids of the hyperbolic quadrics Q^+(7, q)
No full textAn infinite family of (q^2 + q + 1)-ovoids of Q^+(7, q) admitting the group PGL(3,q), is constructed. The main tool is the general theory of generalized hexagons
A clique-free pseudorandom subgraph of the pseudo polarity graph
No full textWe provide a new family of Kk-free pseudorandom graphs with edge density Θ(n−1/(k−1)), matching a recent construction due to Bishnoi, Ihringer and Pepe [2]. As in the former result, the idea is to use large subgraphs of polarity graphs, which are defined over a finite field Fq. While their construction required q to be odd, we will give the first construction with q a power of 2
A note on q-covering designs in PG(5,q)
No full textA construction of q-covering designs in PG(5, q) is given, providing an improvement on the upper bound of the q-covering number (6,3,2)
On symmetric and Hermitian rank distance codes
No full textLet M denote the set Sn,q of n×n symmetric matrices with entries in Fq or the set Hn,qjavax.xml.bind.JAXBElement@3cc3b37d of n×n Hermitian matrices whose elements are in Fqjavax.xml.bind.JAXBElement@232d703c. Then M equipped with the rank distance dr is a metric space. We investigate d–codes in (M,dr) and construct d–codes whose sizes are larger than the corresponding additive bounds. In the Hermitian case, we show the existence of an n–code of M, n even and n/2 odd, of size (3qn−qn/2)/2, and of a 2–code of size q6+q(q−1)(q4+q2+1)/2, for n=3. In the symmetric case, if n is odd, we provide better upper bound on the size of a 2–code. In the case when n=3 and q>2, a 2–code of size q4+q3+1 is exhibited. This provides the first infinite family of 2–codes of symmetric matrices whose size is larger than the largest possible additive 2–code and an answer to a question posed in [25, Section 7], see also [23, p. 176]
INTRIGUING SETS OF STRONGLY REGULAR GRAPHS AND THEIR RELATED STRUCTURES
No full textIn this paper we outline a technique for constructing directed strongly regular graphs by using strongly regular graphs having a “nice” family of intriguing sets. Further, we investigate such a construction method for rank three strongly regular graphs having at most 45 vertices. Finally, several examples of intriguing sets of polar spaces are provided
Subspace code constructions
No full textWe improve on the lower bound of the maximum number of planes of PG (8 , q) mutually intersecting in at most one point leading to the following lower bound: Aq(9 , 4 ; 3) ≥ q12+ 2 q8+ 2 q7+ q6+ q5+ q4+ 1. We also construct two new non–equivalent (6,(q3-1)(q2+q+1),4;3)q–constant dimension subspace orbit–codes
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