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 non-existence of 29+ h, 3+ h, 26 _ 16 29+ h, 3+ h, 26 16 and 29+ h, 4+ h, 25 _ 16 29+ h,
4+ h, 25 16-codes, h ≥ 0 h≥ 0, is proven. These results are obtained using geometrical …

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 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 …

In the projective plane PG (2, q), we consider an iterative construction of complete arcs
which adds a new point in each step. It is proved that uncovered points are uniformly …

In this work we summarize some recent results to be included in a forthcoming paper
[Bartoli, D., AA Davydov, S. Marcugini and F. Pambianco, New types of estimate for the …

New types of upper bounds for the smallest size t 2 (2, q) of a complete arc in the projective
plane PG (2, q) are proposed. The value t_ 2 (2, q)= d (q) q\ln qt 2 (2, q)= d (q) q ln q, where …

For q= pr with a prime p≥ 7 such that q ≡ 1 or 19 (mod 30), the desarguesian projective
plane PG (2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to …

In this work complete caps in PG (N, q) of size O (q^ N-1 2\log^ 300 q) O (q N-1 2 log 300 q)
are obtained by probabilistic methods. This gives an upper bound asymptotically very close …