Two-Point Codes for the Generalized GK Curve
- Resource Type
- Periodical
- Authors
- Barelli, E.; Beelen, P.; Datta, M.; Neiger, V.; Rosenkilde, J.
- Source
- IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 64(9):6268-6276 Sep, 2018
- Subject
- Communication, Networking and Broadcast Technologies
Signal Processing and Analysis
Electronic mail
Cost accounting
Geometry
Linear codes
Scholarships
Europe
AG code
GGK curve
order bound
two-point Weierstrass semigroup
- Language
- ISSN
- 0018-9448
1557-9654
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 certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.