In this work complete caps in PG(N, q) of size O(q^(N−1)/2 log^300 q) are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound √2q^(N−1)/2 and it improves the best known bound in the literature for small complete caps in projective spaces of any dimension. The result obtained in the paper also gives a new upper bound for l(m, 2, q)4, that is the minimal length n for which there exists an [n, n − m, 4]q2 covering code with given m and q.
A construction of small complete caps in projective spaces
BARTOLI, DANIELE;FAINA, Giorgio;MARCUGINI, Stefano
;PAMBIANCO, Fernanda
2017
Abstract
In this work complete caps in PG(N, q) of size O(q^(N−1)/2 log^300 q) are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound √2q^(N−1)/2 and it improves the best known bound in the literature for small complete caps in projective spaces of any dimension. The result obtained in the paper also gives a new upper bound for l(m, 2, q)4, that is the minimal length n for which there exists an [n, n − m, 4]q2 covering code with given m and q.File in questo prodotto:
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