The aim of this paper is to construct cyclic subgroups of the projective general linear group
over 𝐹23 from the companion matrix, and then form caps of various degrees in 𝑃𝐺 (3, 23) …

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 …

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 …

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 …

In the projective plane PG (2, q), upper bounds on the smallest size t 2 (2, q) of a complete
arc are considered. For a wide region of values of q, the results of computer search obtained …

The objective of this paper is to designing computer programs to find points, planes, and
lines, as well as to find mr (3, q) for the projective space PG (3, q), when q is prime, and a …