Small complete caps in Galois affine spaces

The geometry of covering codes: small complete caps and saturating sets in Galois spaces

Constructions of Small Complete Caps in Binary Projective Spaces

In the binary projective spaces PG(n,2) k-caps are called large if k > 2n−1 and small if k ≤ 2n−1. In this paper we propose new constructions producing infinite families of small binary complete caps.

New upper bounds on the smallest size of a complete cap in the space PG(3, q)

In the projective spaces PG(3, q), more than 370 new small complete caps are obtained for q ≤ 3109, q prime. This implies new upper bounds on the smallest size t2(3, q) of a complete cap in PG(3, q). From the new bounds it follows that the relation t2(3, q) < 6q holds for q ∈ R, where R is a set of 400 prime value in the interval [2, 3109]. The new upper bounds are obtained by finding new small...

Minimal 1-saturating sets and complete caps in binary projective spaces

In binary projective spaces PG(v, 2), minimal 1-saturating sets, including sets with inner lines and complete caps, are considered. A number of constructions of the minimal 1-saturating sets are described. They give infinite families of sets with inner lines and complete caps in spaces with increasing dimension. Some constructions produce sets with an interesting symmetrical structure connected...

NEW INDUCTIVE CONSTRUCTIONS OF COMPLETE CAPS IN PG ( N , q ) , q EVEN

Some new families of small complete caps in PG(N, q), q even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in this paper provide an improvement on the currently known upper bounds on the size of the smallest complete cap in PG(N, q...