On Weierstrass semigroups and sets: a review with new results

DOI10.1007/s10711-008-9337-yzbMath1168.14028OpenAlexW1987213283MaRDI QIDQ1018082

Takao Kato, Cícero Fernandes de Carvalho

Publication date: 13 May 2009

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-008-9337-y

zbMATH Keywords

hyperelliptic curveplane curveHermitian curvealgebraic geometric codesWeierstrass semigroupsWeierstrass pointpure gapstotal inflection pointWeierstrass sets

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Curves over finite and local fields (11G20) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (14)

On semigroups, Gröbner basis and algebras admitting a complete set of near weights ⋮ On Weierstrass Semigroups of Some Triples on Norm-Trace Curves ⋮ AG codes and AG quantum codes from the GGS curve ⋮ 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 ⋮ 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 ⋮ Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve ⋮ Weierstrass semigroup and codes over the curve \(y^q + y = x^{q^r + 1}\) ⋮ Lower bounds on the minimum distance in Hermitian one-point differential codes ⋮ AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves ⋮ On the Weierstrass semigroups of \(n\) points of a smooth curve ⋮ On Laplacian Monopoles

Cites Work

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• Algebraic Functions and Projective Curves
• Weierstrass pairs and minimum distance of Goppa codes
• Goppa codes with Weierstrass pairs
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