Let A_ {R, q} denote a family of covering codes, in which the covering radius R and the size
q of the underlying Galois field are fixed, while the code length tends to infinity. In this paper …

A ϱ ϱ-saturating set of PG (N, q) PG (N, q) is a point set SS such that any point of PG (N, q)
PG (N, q) lies in a subspace of dimension at most ϱ ϱ spanned by points of S S. It is …

Complete caps and saturating sets in projective Galois spaces are the geometrical
counterpart of linear codes with covering radius 2. The smaller the cap/saturating set, the …

The length function ℓ _q (r, R) ℓ q (r, R) is the smallest length of aq-ary linear code of
codimension r and covering radius R. In this work we obtain new constructive upper bounds …

Minimal saturating sets in projective spaces PG (n, q) are considered. Estimates and exact
values of some extremal parameters are given. In particular the greatest cardinality of a …

A set of points, S⊆ PG (r, q), is said to be ϱ-saturating if, for any point x∈ PG (r, q), there
exist ϱ+ 1 points in S that generate a subspace in which x lies. The cardinality of a smallest …

Let [n, nr]/sub q/R denote a linear code over F/sub q/with length n, codimension r, and
covering radius R. We use a modification of constructions of [2q+ 1, 2q-3]/sub q/2 and [3q+ …

The length function ℓ q (r, R) is the smallest length of aq-ary linear code of covering radius R
and codimension r. In this work we obtain new upper bounds on ℓ q (2 t+ 1, 2), ℓ q (3 t+ 1, 3) …

The length function ℓ _q (r, R) is the smallest length of aq-ary linear code of covering radius
R and codimension r. New upper bounds on ℓ _q (r, 2) are obtained for odd r ≥ 3. In …

The minimum size of a complete arc in the planes PG (2, 31) and PG (2, 32) and of a 1-
saturating set in PG (2, 17) and PG (2, 19) is determined. Also, the minimal 1-saturating sets …