We consider Erdos-Ko-Rado sets of generators in classical finite polar spaces. These are sets of generators that all intersect non-trivially. We characterize the Erdos-Ko-Rado sets of generators of maximum size in all polar spaces, except for H(4n+1,q^2)...

Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many results in finite geometry were obtained by applying characterization results on minihypers (De Beule et al. 16:342---349, 2008;...

In this paper, we study the p -ary linear code C ( PG ( n , q )), q = p ^h , p prime, h 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG ( n , q ), and its dual code. We link the ...

We present improved lower bounds on the sizes of small maximal partial ovoids and small maximal partial spreads in the classical symplectic and orthogonal polar spaces, and improved upper bounds on the sizes of large maximal partial ovoids and large ...

We present improved lower bounds on the sizes of small maximal partial ovoids in the classical hermitian polar spaces, and improved upper bounds on the sizes of large maximal partial spreads in the classical hermitian polar spaces. Of particular ...

We present results on the size of the smallest maximal partial ovoids and on the size of the smallest maximal partial spreads of the generalized quadrangles W(q) and Q(4,q).

We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in ...

We determine the smallest nontrivial blocking sets with respect to t-spaces in PG(n, 2), n ≥ 3. For t = n - 1, they are skeletons of solids in PG(n, 2); for 1 ≤ t < n - 1, they are cones with vertex an (n - t - 3)- space π_{n-t - 3} and base the set of ...

We determine the smallest minimal blocking sets of Q ⁺ (2 n + 1,3), n 4.

It is known that every ovoid of the parabolic quadric Q(4, q ), q = p ^h , p prime, intersects every three-dimensional elliptic quadric in 1 mod p points. We present a new approach which gives us a second proof of this result and, in the case ...

A lot of research has been done on the spectrum of the sizes of maximal partial spreads in PG (3, q ) [P. Govaerts and L. Storme, Designs Codes and Cryptography , Vol. 28 (2003) pp. 51--63; O. Heden, Discrete Mathematics , Vol. 120 (1993) pp. 75--91;...

This article classifies all {ý( q + 1), ý; 3, q }-minihypers, ý small, q = p ^h ₀, h ý 1, for a prime number p ₀ ý 7, which arise from a maximal partial spread of deficiency ý. When q is a third power, the minihyper is the disjoint union of ...

Two ways of constructing maximal sets of mutually orthogonal Latin squares are presented.

The first construction uses maximal partial spreads in PG(3, 4) \ PG(3, 2) with r lines, where r ∈ {6, 7}, to construct transversal-free translation nets of order ...

In this article we give a Griesmer type bound for linear codes over finite quasi-Frobenius rings and consider linear codes over these rings meeting the bound. And we study a geometrical characterization of linear codes over finite chain rings meeting ...

Assuming a partial spread of T₂(O) or T₃(O), with deficiency δ, is maximal and using results on minihypers, which are closely related to blocking sets in PG(2, q), we obtain lower bounds for δ. If q is even, using extendability of arcs in PG(2, q), we ...

In the first two articles of this series, the structure of certain minihypers was determined. Hamada shows how these results translate into results on linear codes meeting the Griesmer bound, while Govaerts and Storme show how they can be applied to ...

A i&gt;t-cover of a quadric {\cal Q} is a set {\cal C} of i&gt;t-dimensional subspaces contained in {\cal Q} such that every point of {\cal Q} is contained in at least one element of {\cal C} .

We consider (i&gt;n ý 1)-covers of the hyperbolic quadric i&...

A particular class of minihypers was studied previously by the authors (in press, Des. Codes Cryptogr.). For q square, this paper improves the results of that work, under the assumption that no weights occur in the minihyper. Using the link between ...

We extend the results of Polverino (1999, Discrete Math., 208/209, 469 476; 2000, Des. Codes Cryptogr., 20, 319 324) on small minimal blocking sets in PG(2,p3 ), p prime, p 7, to small minimal blocking sets inPG (2, q3), q=ph, p prime, p 7, with ...

In this paper, i&gt;k-blocking sets in i&gt;PG(i&gt;n, i&gt;q), being of Rédei type, are investigated. A standard method to construct Rédei type i&gt;k-blocking sets in i&gt;PG(i&gt;n, i&gt;q) is to construct a cone having as base a Rédei type i&gt;ký-...