On curves covered by the Hermitian curve.
From MaRDI portal
Publication:1293103
DOI10.1006/jabr.1998.7768zbMath1054.14026OpenAlexW2804993108MaRDI QIDQ1293103
Fernando Torres, Gábor Korchmáros, Antonio Cossidente
Publication date: 28 February 2000
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jabr.1998.7768
Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15)
Related Items
Quotient curves of the GK curve ⋮ Some Maximal Function Fields and Additive Polynomials ⋮ On some open problems on maximal curves ⋮ Quantum error-correcting codes from algebraic geometry codes of castle type ⋮ Some Ree and Suzuki curves are not Galois covered by the Hermitian curve ⋮ Hermitian codes from higher degree places ⋮ On maximal curves which are not Galois subcovers of the Hermitian curve ⋮ Multi-point codes over Kummer extensions ⋮ On subfields of the Hermitian function field involving the involution automorphism ⋮ On space maximal curves ⋮ An \(\mathbb{F}_{p^2 } \)-maximal Wiman sextic and its automorphisms ⋮ A new family of maximal curves over a finite field ⋮ On maximal curves that are not quotients of the Hermitian curve ⋮ Collineation groups of the intersection of two classical unitals ⋮ Quotients of the Hermitian curve from subgroups of \(\text{PGU}(3,q)\) without fixed points or triangles ⋮ On the spectrum for the genera of maximal curves over small fields ⋮ On the spectrum of genera of quotients of the Hermitian curve ⋮ Curves covered by the Hermitian curve ⋮ The complete list of genera of quotients of the \(\mathbb{F}_{q^2}\)-maximal Hermitian curve for \(q \equiv 1 \pmod 4\) ⋮ Further examples of maximal curves ⋮ Maximal hyperelliptic curves of genus three ⋮ Quadratic forms of codimension 2 over finite fields containing \(\mathbb F_4\) and Artin-Schreier type curves ⋮ On the classification problem for the genera of quotients of the Hermitian curve ⋮ Classification of all Galois subcovers of the Skabelund maximal curves ⋮ Curves of large genus covered by the hermitian curve
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weierstrass points on certain non-classical curves
- Generalized Reed-Muller codes and curves with many points
- On the number of rational points on an algebraic curve over a finite field
- On maximal curves in characteristic two
- The genus of maximal function fields over finite fields
- On maximal curves
- On the embedding of an arc into a conic in a finite plane
- A new proof of the existence of \((q^ 2-q+1)\)-arcs in \(PG(2,q^ 2)\)
- The genus of curves over finite fields with many rational points
- Zur arithmetischen Theorie der algebraischen Funktionen. II: Allgemeine Theorie der Weierstraßpunkte
- ALGEBRAICO-GEOMETRIC CODES
- Weierstrass Points and Curves Over Finite Fields
- On the linear diophantine problem of Frobenius.
- On Weierstrass points and optimal curves
- A characterization of Hermitian function fields over finite fields.
- How to Construct Curves over Finite Fields With Many Points
- On certain n-sheeted coverings of curves and numerical semigroups which cannot be realized as weierstrass semigroups
- Algebraic function fields over finite fields with many rational places