scholarly journals Automorphisms of curves and Weierstrass semigroups for Harbater–Katz–Gabber covers

2019 ◽  
Vol 371 (9) ◽  
pp. 6377-6402 ◽  
Author(s):  
Sotiris Karanikolopoulos ◽  
Aristides Kontogeorgis
Keyword(s):  
Weierstrass Semigroups

scholarly journals Ideals of Numerical Semigroups and Error-Correcting Codes

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1406
Author(s):  
Bras-Amorós
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Numerical Semigroups ◽  
Secret Sharing Schemes ◽  
List Decoding ◽  
Generalized Hamming Weights ◽  
Resilient Functions ◽  
Weierstrass Semigroups ◽  
Hamming Weights ◽  
Dual Sequences

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

scholarly journals Weierstrass semigroups on the Giulietti–Korchmáros curve

2018 ◽  
Vol 52 ◽  
pp. 10-29 ◽  
Author(s):  
Peter Beelen ◽  
Maria Montanucci
Keyword(s):  
Weierstrass Semigroups

scholarly journals Generalized Weierstrass semigroups and their Poincaré series

2019 ◽  
Vol 58 ◽  
pp. 46-69
Author(s):  
J.J. Moyano-Fernández ◽  
W. Tenório ◽  
F. Torres
Keyword(s):  
Poincaré Series ◽  
Poincare Series ◽  
Weierstrass Semigroups

scholarly journals The Weierstrass semigroups on double covers of genus two curves

2015 ◽  
Vol 38 (2) ◽  
pp. 201-206
Author(s):  
Takeshi Harui ◽  
Jiryo Komeda ◽  
Akira Ohbuchi
Keyword(s):  
Weierstrass Semigroups ◽  
Double Covers ◽  
Genus Two

scholarly journals AG codes from $${{\mathbb{F}}_{q^7}}$$-rational points of the GK maximal curve

2021 ◽  
Author(s):  
Stefano Lia ◽  
Marco Timpanella
Keyword(s):  
Finite Fields ◽  
Minimum Distance ◽  
Rational Points ◽  
Quantum Codes ◽  
Ag Codes ◽  
Maximal Curve ◽  
Weierstrass Semigroups ◽  
Minimal Generators

AbstractIn Beelen and Montanucci (Finite Fields Appl 52:10–29, 2018) and Giulietti and Korchmáros (Math Ann 343:229–245, 2009), Weierstrass semigroups at points of the Giulietti–Korchmáros curve $${\mathcal {X}}$$ X were investigated and the sets of minimal generators were determined for all points in $${\mathcal {X}}(\mathbb {F}_{q^2})$$ X ( F q 2 ) and $${\mathcal {X}}(\mathbb {F}_{q^6})\setminus {\mathcal {X}}( \mathbb {F}_{q^2})$$ X ( F q 6 ) \ X ( F q 2 ) . This paper completes their work by settling the remaining cases, that is, for points in $${\mathcal {X}}(\overline{\mathbb {F}}_{q}){\setminus }{\mathcal {X}}( \mathbb {F}_{q^6})$$ X ( F ¯ q ) \ X ( F q 6 ) . As an application to AG codes, we determine the dimensions and the lengths of duals of one-point codes from a point in $${\mathcal {X}}(\mathbb {F}_{q^7}){\setminus }{\mathcal {X}}( \mathbb {F}_{q})$$ X ( F q 7 ) \ X ( F q ) and we give a bound on the Feng–Rao minimum distance $$d_{ORD}$$ d ORD . For $$q=3$$ q = 3 we provide a table that also reports the exact values of $$d_{ORD}$$ d ORD . As a further application we construct quantum codes from $$\mathbb {F}_{q^7}$$ F q 7 -rational points of the GK-curve.

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