Elementary abelian \(p\)-extensions of algebraic function fields

DOI10.1007/BF02568266zbMath0739.14015OpenAlexW2060261598MaRDI QIDQ1814168

Arnaldo Garcia, Henning Stichtenoth

Publication date: 25 June 1992

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155629

zbMATH Keywords

characteristic \(p\)genuscoding theorynumber of rational pointsArtin-Schreier theory\(p\)-extensions of algebraic function fieldsgap number

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Computational aspects of algebraic curves (14Q05) Riemann surfaces; Weierstrass points; gap sequences (14H55) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items

Complete \((k,3)\)-arcs from quartic curves, A BOUND ON THE NUMBER OF RATIONAL POINTS OF CERTAIN ARTIN-SCHREIER FAMILIES, Genus formulas for abelian \(p\)-extensions, Switchings of semifield multiplications, A More General Framework for CoGalois Theory, AG codes from vector bundles, Generalising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem, On maximal curves, Two applications of Weil-Serre's explicit formula, A cohomological treatise of HKG-covers with applications to the Nottingham group, Galois module structure of holomorphic differentials in characteristic \(p\), A new family of Castle and Frobenius nonclassical curves, Complete \((k,4)\)-arcs from quintic curves, Algebraic constructions of complete \(m\)-arcs, Boomerang uniformity of power permutations and algebraic curves over \(\mathbb{F}_{2^n}\), On the moments of Kloosterman sums and fibre products of Kloosterman curves, On cohomology of generalized Suzuki curves and exponential sums, Abelian p-extensions and additive polynomials, On geometric Goppa codes from elementary abelian \(p\)-extensions of \(\mathbb{F}_{p^s}(x)\), Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients pre\-scribed, Multidimensional cyclic codes and Artin-Schreier type hypersurfaces over finite fields, The discriminant problem for Artin-Schreier extensions: explicit results, Genus fields of abelian extensions of rational congruence function fields. II, Elements of prescribed order, prescribed traces and systems of rational functions over finite fields, Improvements on generalized Hamming weights of some trace codes, THE RAMIFICATION GROUPS AND DIFFERENT OF A COMPOSITUM OF ARTIN–SCHREIER EXTENSIONS, On automorphism groups of certain Goppa codes, On the Zeta function and the automorphism group of the generalized Suzuki curve, Large \(p\)-group actions with a \(p\)-elementary abelian derived group, A class of polynomials over finite fields, Arithmetic of abelian varieties in Artin-Schreier extensions, The 𝑎-numbers of Jacobians of Suzuki curves, Weierstrass semigroups at every point of the Suzuki curve, Galois module structure of holomorphic differentials, Curves of every genus with many points. I: Abelian and toric families., Coverings of curves with asymptotically many rational points

Cites Work

• Unnamed Item
• Weierstrass points in characteristic p
• Weierstrass points on certain non-classical curves
• A study of Hasse-Witt matrices by local methods
• Self-dual Goppa codes
• Artin-Schreier curves, exponential sums, and the Carlitz-Uchiyama bound for geometric codes
• Algebraic curves with non-classical types of gap sequences for genus three and four
• Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. I: Eine Abschätzung der Ordnung der Automorphismengruppe
• Group codes on certain algebraic curves with many rational points
• Zur arithmetischen Theorie der algebraischen Funktionen. II: Allgemeine Theorie der Weierstraßpunkte
• Relations Between the Genera and Between the Hasse-Witt Invariants of Galois Coverings of Curves
• The number of points on certain algebraic curves over finite fields
• ALGEBRAICO-GEOMETRIC CODES
• Funktionenkörper mit großer Automorphismengruppe.
• Zyklische unverzweigte Erweiterungskörper vom Primzahlgradep über einem algebraischen Funktionenkörper der Charakteristikp