On Goppa codes and Weierstrass gaps at several points
From MaRDI portal
Publication:1781001
DOI10.1007/s10623-005-6403-4zbMath1070.94029OpenAlexW1997825023MaRDI QIDQ1781001
Fernando Torres, Cícero Fernandes de Carvalho
Publication date: 15 June 2005
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10623-005-6403-4
Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Riemann surfaces; Weierstrass points; gap sequences (14H55) Applications to coding theory and cryptography of arithmetic geometry (14G50)
Related Items (45)
Bases of Riemann-Roch spaces from Kummer extensions and algebraic geometry codes ⋮ On \(\mathcal V\)-Weierstrass sets and gaps ⋮ Non-special subsets of the set of points of a curve defined over a finite field ⋮ On semigroups, Gröbner basis and algebras admitting a complete set of near weights ⋮ New lower bounds for the minimum distance of generalized algebraic geometry codes ⋮ Algebraic geometric codes on many points from Kummer extensions ⋮ Pure gaps on curves with many rational places ⋮ Weierstrass semigroups from Kummer extensions ⋮ On Weierstrass Semigroups of Some Triples on Norm-Trace Curves ⋮ Weierstrass semigroup and pure gaps at several points on the \(GK\) curve ⋮ AG codes and AG quantum codes from the GGS curve ⋮ Multi-point codes from the GGS curves ⋮ Hermitian codes from higher degree places ⋮ Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve ⋮ Isometry-Dual Flags of Many-Point AG Codes ⋮ An approach to the bases of Riemann-Roch spaces ⋮ Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables ⋮ Generalized Weierstrass semigroups and their Poincaré series ⋮ On Weierstrass gaps at several points ⋮ Multi-point codes over Kummer extensions ⋮ Pure Weierstrass gaps from a quotient of the Hermitian curve ⋮ Complete set of pure gaps in function fields ⋮ On Multi-Index Filtrations Associated to Weierstraß Semigroups ⋮ Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve ⋮ On Weierstrass semigroup at \(m\) points on curves of the form \(f(y)=g(x)\) ⋮ Lower bounds on the minimum distance in Hermitian one-point differential codes ⋮ On Weierstrass semigroups at one and two points and their corresponding Poincaré series ⋮ Two-Point Codes on Norm-Trace Curves ⋮ The structure of algebras admitting well-agreeing near weights ⋮ Further improvements on the designed minimum distance of algebraic geometry codes ⋮ AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves ⋮ Weierstrass gaps at \(n\) points of a curve ⋮ Distance bounds for algebraic geometric codes ⋮ Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences ⋮ Weierstrass semigroups and codes from a quotient of the Hermitian curve ⋮ On the Weierstrass semigroups of \(n\) points of a smooth curve ⋮ Triples of rational points on the Hermitian curve and their Weierstrass semigroups ⋮ Hermitian codes with automorphism group isomorphic to \(\operatorname{PGL}(2,q)\) with \(q\) odd ⋮ Codes from curves with total inflection points ⋮ Weierstrass semigroup and automorphism group of the curves \(\mathcal{X}_{n,r}\) ⋮ On Weierstrass semigroups and sets: a review with new results ⋮ On algebras admitting a complete set of near weights, evaluation codes, and Goppa codes ⋮ Weierstrass points on Kummer extensions ⋮ Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be covered by the Hermitian curve ⋮ On the floor and the ceiling of a divisor
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weierstrass points on certain non-classical curves
- Fermat curves over finite fields
- Consecutive Weierstrass gaps and minimum distance of Goppa codes
- Weierstrass multiple loci of \(n\)-pointed algebraic curves
- The Weierstrass semigroup of a pair of Galois Weierstrass points with prime degree on a curve
- On the index of the Weierstrass semigroup of a pair of points on a curve
- The genus of curves over finite fields with many rational points
- The Weierstrass semigroup of a pair of points on a curve
- ALGEBRAICO-GEOMETRIC CODES
- A note on Hermitian codes over GF(q/sup 2/)
- On the weight hierarchy of geometric Goppa codes
- Weierstrass pairs and minimum distance of Goppa codes
- Goppa codes with Weierstrass pairs
This page was built for publication: On Goppa codes and Weierstrass gaps at several points
