scholarly journals Complete arcs arising from a generalization of the Hermitian curve

2014 ◽  
Vol 164 (2) ◽  
pp. 101-118 ◽  
Author(s):  
Herivelto Borges ◽  
Beatriz Motta ◽  
Fernando Torres
Keyword(s):  
Hermitian Curve ◽  
Complete Arcs

scholarly journals A class of complete arcs in multiply derived planes

2003 ◽  
Vol 3 (s1) ◽  
Author(s):  
Arrigo Bonisoli ◽  
Gloria Rinaldi
Keyword(s):  
Complete Arcs

𝔽 p 2 -maximal curves with many automorphisms are Galois-covered by the Hermitian curve

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Daniele Bartoli ◽  
Maria Montanucci ◽  
Fernando Torres
Keyword(s):  
Finite Field ◽  
Prime Numbers ◽  
Hermitian Curve ◽  
Maximal Curve ◽  
Maximal Curves

Abstract Let 𝔽 be the finite field of order q 2. It is sometimes attributed to Serre that any curve 𝔽-covered by the Hermitian curve H q + 1 : y q + 1 = x q + x ${{\mathcal{H}}_{q+1}}:{{y}^{q+1}}={{x }^{q}}+x$ is also 𝔽-maximal. For prime numbers q we show that every 𝔽-maximal curve x $\mathcal{x}$ of genus g ≥ 2 with | Aut(𝒳) | > 84(g − 1) is Galois-covered by H q + 1 . ${{\mathcal{H}}_{q+1}}.$ The hypothesis on | Aut(𝒳) | is sharp, since there exists an 𝔽-maximal curve x $\mathcal{x}$ for q = 71 of genus g = 7 with | Aut(𝒳) | = 84(7 − 1) which is not Galois-covered by the Hermitian curve H 72 . ${{\mathcal{H}}_{72}}.$

The Complete Arcs of PG(2,31)

2014 ◽  
Vol 23 (12) ◽  
pp. 522-533 ◽  
Author(s):  
Kris Coolsaet
Keyword(s):  
Complete Arcs

scholarly journals On small complete arcs in a finite plane

1997 ◽  
Vol 174 (1-3) ◽  
pp. 29-34 ◽  
Author(s):  
Simeon Ball
Keyword(s):  
Finite Plane ◽  
Complete Arcs

On the minimum size of complete arcs and minimal saturating sets in projective planes

2013 ◽  
Vol 104 (3) ◽  
pp. 409-419 ◽  
Author(s):  
Daniele Bartoli ◽  
Giorgio Faina ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Projective Planes ◽  
Minimum Size ◽  
Complete Arcs

Small complete arcs in andré planes of square order

1991 ◽  
Vol 7 (3) ◽  
pp. 279-287
Author(s):  
Tamás Szönyi
Keyword(s):  
Complete Arcs
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