In the projective plane PG(2,q), q=2 (mod 3) odd power prime, q<=11, an explicit construction of ((q+7)/2)-arcs sharing (q+3)/2 points with an irreducible conic is considered. The construction is based on 3-orbits of some projectivity, called 3-cycles. For every q, variants of the construction give non equivalent arcs. It allows us to obtain complete ((q+7)/2)-arcs for q<= 4523. Moreover, for q=17,59 there exist variants that are incomplete arcs. Completing these variants we obtained complete ((q+3)/2+delta )-arcs with delta =4, q=17, and delta =3, q=59; a description of them as union of some symmetrical objects is given.
A geometric construction of complete arcs sharing (q+3)/2 points with a conic
MARCUGINI, Stefano;PAMBIANCO, Fernanda
2010
Abstract
In the projective plane PG(2,q), q=2 (mod 3) odd power prime, q<=11, an explicit construction of ((q+7)/2)-arcs sharing (q+3)/2 points with an irreducible conic is considered. The construction is based on 3-orbits of some projectivity, called 3-cycles. For every q, variants of the construction give non equivalent arcs. It allows us to obtain complete ((q+7)/2)-arcs for q<= 4523. Moreover, for q=17,59 there exist variants that are incomplete arcs. Completing these variants we obtained complete ((q+3)/2+delta )-arcs with delta =4, q=17, and delta =3, q=59; a description of them as union of some symmetrical objects is given.File in questo prodotto:
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