The number of rational points of a class of Artin-Schreier curves.
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Publication:1867453
DOI10.1006/ffta.2001.0348zbMath1056.11038OpenAlexW2017272993MaRDI QIDQ1867453
Publication date: 2 April 2003
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/ffta.2001.0348
Rational points (14G05) Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Exponential sums (11T23)
Related Items (23)
Further results on rational points of the curve \(y^{q^n}-y=\gamma x^{q^h+1}-\alpha \) over \(\mathbb F_{q^m}\) ⋮ A family of optimal ternary cyclic codes with minimum distance five and their duals ⋮ Weight distributions of two classes of linear codes with five or six weights ⋮ On the number of solutions of certain diagonal equations over finite fields ⋮ New cyclic difference sets with Singer parameters ⋮ Exact evaluation of second moments associated with some families of curves over a finite field ⋮ Artin-Schreier curves given by \(\mathbb{F}_q\)-linearized polynomials ⋮ Quadratic functions and maximal Artin-Schreier curves ⋮ Reciprocal polynomials and curves with many points over a finite field ⋮ On the number of rational points on Artin-Schreier hypersurfaces ⋮ Two classes of new optimal ternary cyclic codes ⋮ The number of rational points of a class of superelliptic curves ⋮ Divisibility of L-polynomials for a family of Artin-Schreier curves ⋮ More on quadratic functions and maximal Artin-Schreier curves ⋮ Curves related to Coulter's maximal curves ⋮ A construction of a class of maximal Kummer curves. ⋮ A new family of maximal curves over a finite field ⋮ Constructions of several classes of linear codes with a few weights ⋮ The subfield codes of several classes of linear codes ⋮ A class of subfield codes of linear codes and their duals ⋮ Binary linear codes with few weights from Boolean functions ⋮ Complete weight enumerators of a class of two-weight linear codes ⋮ Complete weight enumerators of a class of linear codes with two or three weights
Cites Work
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- Algebraic function fields and codes
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- The genus of curves over finite fields with many rational points
- The number of points on certain algebraic curves over finite fields
- Further evaluations of Weil sums
- A characterization of Hermitian function fields over finite fields.
- On the Existence of Supersingular Curves of Given Genus
- Explicit evaluations of some Weil sums
- Polars of Artin-Schreier curves
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