Journal article
M. Giulietti, G. Korchmáros, S. Marcugini, F. Pambianco
Des. Codes Cryptogr., 2011
Des. Codes Cryptogr., 2011
Semantic Scholar
ArXiv
DBLP
DOI
Cite
Cite
APA
Click to copy
Giulietti, M., Korchmáros, G., Marcugini, S., & Pambianco, F. (2011). Transitive A6-invariant k-arcs in PG(2, q). Des. Codes Cryptogr.
Chicago/Turabian
Click to copy
Giulietti, M., G. Korchmáros, S. Marcugini, and F. Pambianco. “Transitive A6-Invariant k-Arcs in PG(2, q).” Des. Codes Cryptogr. (2011).
MLA
Click to copy
Giulietti, M., et al. “Transitive A6-Invariant k-Arcs in PG(2, q).” Des. Codes Cryptogr., 2011.
BibTeX Click to copy
@article{m2011a,
title = {Transitive A6-invariant k-arcs in PG(2, q)},
year = {2011},
journal = {Des. Codes Cryptogr.},
author = {Giulietti, M. and Korchmáros, G. and Marcugini, S. and Pambianco, F.}
}
Abstract
For q = pr with a prime p ≥ 7 such that $${q \equiv 1}$$ or 19 (mod 30), the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to the alternating group A6 of degree 6. For a projectivity group $${\Gamma \cong A_6}$$ of PG(2, q), we investigate the geometric properties of the (unique) Γ-orbit $${\mathcal{O}}$$ of size 90 such that the 1-point stabilizer of Γ in its action on $${\mathcal O}$$ is a cyclic group of order 4. Here $${\mathcal O}$$ lies either in PG(2, q) or in PG(2, q2) according as 3 is a square or a non-square element in GF(q). We show that if q ≥ 349 and q ≠ 421, then $${\mathcal O}$$ is a 90-arc, which turns out to be complete for q = 349, 409, 529, 601,661. Interestingly, $${\mathcal O}$$ is the smallest known complete arc in PG(2,601) and in PG(2,661). Computations are carried out by MAGMA.
