# On line covers of finite projective and polar spaces

@article{Cossidente2019OnLC,
title={On line covers of finite projective and polar spaces},
author={Antonio Cossidente and Francesco Pavese},
journal={Designs, Codes and Cryptography},
year={2019},
pages={1-18}
}
• Published 30 June 2018
• Mathematics, Computer Science
• Designs, Codes and Cryptography
An m-cover of lines of a finite projective space $$\mathrm{PG}(r,q)$$PG(r,q) (of a finite polar space $${\mathcal {P}}$$P) is a set of lines $${\mathcal {L}}$$L of $$\mathrm{PG}(r,q)$$PG(r,q) (of $${\mathcal {P}}$$P) such that every point of $$\mathrm{PG}(r,q)$$PG(r,q) (of $${\mathcal {P}}$$P) contains m lines of $${\mathcal {L}}$$L, for some m. Embed $$\mathrm{PG}(r,q)$$PG(r,q) in $$\mathrm{PG}(r,q^2)$$PG(r,q2). Let $${{\bar{{\mathcal {L}}}}}$$L¯ denote the set of points of $$\mathrm{PG}(r,q^2… 1 Citations ## Topics from this paper Constructions of tight sets of the Hermitian polar space \mc{H}(2r-1,q^2) In this paper, we construct two infinite families of tight sets with parameters (q − 1) and (q − q), respectively, in the Hermitian polar space H(2r − 1, q) for any r ≥ 2 and any prime power q. Both ## References SHOWING 1-10 OF 31 REFERENCES Hemisystems on the Hermitian Surface • Mathematics • 2005 The natural geometric setting of quadrics commuting with a Hermitian surface of {\rm PG}(3,q^2) , q odd, is adopted and a hemisystem on the Hermitian surface {\cal H}(3,q^2) admitting the group On the Orbits of Singer Groups and Their Subgroups • Keldon Drudge • Mathematics, Computer Science Electron. J. Comb. • 2002 This paper studies the action of Singer groups of projective geometries (and their subgroups) on (d-1)-flats for arbitrary d and determines the maximum co-dimension of f_q(n, h) of a flat of PG(n-1, q) whose orbit under a subgroup of index h of some Singer group covers all points of £PG (n- 1, q). On the Smallest Non-Trivial Tight Sets in Hermitian Polar Spaces • Mathematics • 2017 We show that an x-tight set of the Hermitian polar spaces \mathrm{H}(4,q^2) and \mathrm{H}(6,q^2) respectively, is the union of x disjoint generators of the polar space provided that x is Some constructions on the Hermitian surface • A. Cossidente • Mathematics, Computer Science Des. Codes Cryptogr. • 2009 In the geometric setting of commuting orthogonal and unitary polarities, an infinite family of complete (q + 1)2–spans of the Hermitian surface is constructed. The geometry of some two-character sets • Computer Science, Mathematics Des. Codes Cryptogr. • 2008 A projective (n, d, w1, w2)q set (or a two-character set for short) is a set$${\mathcal{S}} of n points of PG(d − 1, q) with the properties that the set generates PG(d − 1, q) and that every
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