scholarly journals On maximal curves which are not Galois subcovers of the Hermitian curve

2012 ◽  
Vol 43 (3) ◽  
pp. 453-465 ◽  
Author(s):  
Iwan Duursma ◽  
Kit-Ho Mak
Keyword(s):  
Hermitian Curve ◽  
Maximal Curves

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 . ${{\mathcal{H}}_{72}}.$

scholarly journals On maximal curves that are not quotients of the Hermitian curve

2016 ◽  
Vol 41 ◽  
pp. 72-88 ◽  
Author(s):  
Massimo Giulietti ◽  
Maria Montanucci ◽  
Giovanni Zini
Keyword(s):  
Hermitian Curve ◽  
Maximal Curves

Further examples of maximal curves which cannot be covered by the Hermitian curve

2016 ◽  
Vol 220 (3) ◽  
pp. 1122-1132 ◽  
Author(s):  
Saeed Tafazolian ◽  
Arnoldo Teherán-Herrera ◽  
Fernando Torres
Keyword(s):  
Hermitian Curve ◽  
Maximal Curves

scholarly journals Curves related to Coulter's maximal curves

2008 ◽  
Vol 14 (1) ◽  
pp. 209-220 ◽  
Author(s):  
Emrah Çakçak ◽  
Ferruh Özbudak
Keyword(s):  
Maximal Curves

scholarly journals A new family of maximal curves

2018 ◽  
Vol 98 (3) ◽  
pp. 573-592 ◽  
Author(s):  
Peter Beelen ◽  
Maria Montanucci
Keyword(s):  
New Family ◽  
Maximal Curves

scholarly journals The automorphism groups of a family of maximal curves

2012 ◽  
Vol 361 ◽  
pp. 92-106 ◽  
Author(s):  
Robert Guralnick ◽  
Beth Malmskog ◽  
Rachel Pries
Keyword(s):  
Automorphism Groups ◽  
Maximal Curves
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