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 …

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 …

More than thirty new upper bounds on the smallest size t 2 (2, q) of a complete arc in the
plane PG (2, q) are obtained for (169≤ q≤ 839. New upper bounds on the smallest size t 2 …

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 …

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 new family of small complete caps in PG (N, q), q even, is constructed. Apart from small
values of either N or q, it provides an improvement on the currently known upper bounds on …

Some new families of caps in Galois affine spaces AG (N, q) of dimension N≡ 0 (mod 4) and
odd order q are constructed. Such caps are proven to be complete by using some new ideas …

Based on the classification of superregular matrices, the numbers of non‐equivalent n‐arcs
and complete n‐arcs in PG (r, q) are determined (i) for 4≤ q≤ 19, 2≤ r≤ q− 2 and arbitrary …

New upper bounds on the smallest size t2 (2, q) of a complete arc in the projective plane PG
(2, q) are obtained for 853≤ q≤ 5107 and q∈ T1∪ T2, where T1={173,181,193,229,243,257,271,277,293,343 …

In the projective planes PG (2, q), more than 1230 new small complete arcs are obtained for
q ≦ 13627 and q ∈ G where G is a set of 38 values in the range 13687,..., 45893; also, 2 …