For projective spaces PG(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 PG(3,2^{h}) is described. In PG(2,q), for q=17, delta =4, and q=19,27, delta =3, we give complete (frac{1}{2} (q+3)+delta )-arcs other than conics and sharing frac{1}{2}(q+3) points with an irreducible conic. We have proven they are unique up to collineations.
On the spectrum of sizes of complete caps in projective spaces PG(n,q) of small dimension
FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2008
Abstract
For projective spaces PG(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 PG(3,2^{h}) is described. In PG(2,q), for q=17, delta =4, and q=19,27, delta =3, we give complete (frac{1}{2} (q+3)+delta )-arcs other than conics and sharing frac{1}{2}(q+3) points with an irreducible conic. We have proven they are unique up to collineations.File in questo prodotto:
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