Giorgio Faina

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A concept of locally optimal (LO) linear covering codes is introduced in accordance with the concept of minimal saturating sets in projective spaces over …nite …elds. An LO code is nonshortening in the sense that removing any column from a parity check matrix we increase the code covering radius. Constructions and in…nite families of LO codes are described.(More)
More than thirty new upper bounds on the smallest size t2(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 t2(n, q) of the complete cap in the space PG(n, q) are given for n = 3 and 25 The bounds are obtained by computer search for new small complete arcs and caps. New upper bounds on the(More)
On the spectrum of sizes of complete caps in projective spaces PG(n,q) of small dimension Abstract. For projective spaces P G(n, q) of small dimension, new sizes of complete caps including small these are obtained. The corresponding tables are given. A generalization of Segre's construction of complete caps in P G(3, 2 h) is described. In P G(2, q), for q =(More)