Intersections between the norm-trace curve and some low degree curves

  title={Intersections between the norm-trace curve and some low degree curves},
  author={Matteo Bonini and Massimiliano Sala},
Rational points on cubic surfaces and AG codes from the Norm-Trace curve
A complete characterization of the intersections between the Norm-Trace curve over Fq3 and the curves of the form y = ax 3 + bx + cx+ d is given, generalizing a previous result by Bonini and Sala and derive some general bounds for the number of rational points on a cubic surface defined over FQ3.
On the weights of dual codes arising from the GK curve
The minimum distance and the minimum weight codewords of dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve are computed and the generalized Hamming weights of such codes are investigated.
Quantum codes from one-point codes on norm-trace curves
  • Boran Kim
  • Computer Science
    Cryptography and Communications
  • 2022


The minimum weights of two-point AG codes on norm-trace curves
On the Hermitian curve and its intersections with some conics
Intersections of Algebraic Curves and their link to the weight enumerators of Algebraic-Geometric Codes
This thesis construct and investigate algebraic geometry codes (shortly AG codes), their parameters and automorphism groups, and investigates maximal curves attaining the Hasse-Weil upper bound for the number of rational points compared with the genus of the curve.
Remarks on codes from Hermitian curves
Parameters and generator matrices are given for the codes obtained by applying Goppa's algebraic-geometric construction method to Hermitian curves in PG (2,q) , where q = 2^{2s} for some s\in {\bf N}
AG codes and AG quantum codes from the GGS curve
The Weierstrass semigroup at all Fq2-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group.
Minimum-weight codewords of the Hermitian codes are supported on complete intersections
On codes from norm-trace curves
The Lang–Weil Estimate for Cubic Hypersurfaces
  • T. Browning
  • Mathematics
    Canadian Mathematical Bulletin
  • 2013
Abstract An improved estimate is provided for the number of ${{\text{F}}_{q}}$ -rational points on a geometrically irreducible, projective, cubic hypersurface that is not equal to a cone.
Cubic forms; algebra, geometry, arithmetic
Arithmetic on Singular Del Pezzo Surfaces
The study of singular cubic surfaces is quite an old subject, since their classification (over C) goes back to Schlafli [39] and Cay ley [8]. However, a recent account by Bruce and Wall [6] has shown