In the projective plane PG(2, q); q = 2 ( mod 3) odd prime power, q >= 11; an explicit construction of 1/2 (q + 7)-arcs sharing 1/2 (q + 3) 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 1/2 (q + 7)-arcs for q <= 4523: Moreover, for q = 17, 59 there exist variants that are incomplete arcs. Completing these variants we obtained complete ( 1/2 (q +3)+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 3-CYCLE CONSTRUCTION OF COMPLETE ARCS SHARING (q + 3)/2 POINTS WITH A CONIC
BARTOLI, DANIELE;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2013
Abstract
In the projective plane PG(2, q); q = 2 ( mod 3) odd prime power, q >= 11; an explicit construction of 1/2 (q + 7)-arcs sharing 1/2 (q + 3) 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 1/2 (q + 7)-arcs for q <= 4523: Moreover, for q = 17, 59 there exist variants that are incomplete arcs. Completing these variants we obtained complete ( 1/2 (q +3)+delta)-arcs with delta = 4, q = 17, and delta = 3, q = 59; a description of them as union of some symmetrical objects is given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
