# Two-Point Codes for the Generalized GK Curve

@article{Barelli2018TwoPointCF, title={Two-Point Codes for the Generalized GK Curve}, author={{\'E}lise Barelli and Peter Beelen and Mrinmoy Datta and Vincent Neiger and Johan Sebastian Rosenkilde}, journal={IEEE Transactions on Information Theory}, year={2018}, volume={64}, pages={6268-6276} }

We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve. Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study…

## 4 Citations

### Multi-point Codes from the GGS Curves

- Computer Science, MathematicsAdv. Math. Commun.
- 2020

The Weierstrass semigroups and pure gaps are characterized explicitly and the floor of a certain type of divisor is determined and the properties of AG codes from GGS curves are investigated.

### Two-point AG codes from the Beelen-Montanucci maximal curve

- Computer ScienceFinite Fields Their Appl.
- 2022

### New Non-Equivalent (Self-Dual) MDS Codes From Elliptic Curves

- Computer ScienceArXiv
- 2022

New non-equivalent MDS and almost MDS codes from elliptic curve codes are constructed and the application to MDS entanglement-assisted quantum codes is given.

### On the security of short McEliece keys from algebraic and algebraic geometry codes with automorphisms. (Étude de la sécurité de certaines clés compactes pour le schéma de McEliece utilisant des codes géométriques)

- Computer Science
- 2018

It is shown that it is possible to reduce the key-recovery problem on the original quasi-cyclic code to the same problems on the invariant code, and this result permits us to propose a security analysis of QC codes coming from the Hermitian curve.

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