On the intersection of curves and their link to the weight enumerators of algebraic-geometric codes

Luogo: PovoZero, via Sommarive, 14 - Povo - Sala Seminari 1
Ore: 15:00

Relatore: 

• Bonini Matteo (PhD Student in Mathematics)

Abstract:

One of the most difficult problems in coding theory is the determination of the weight distribution of a given linear code. In the case of algebraic-geometric codes sometimes it is possible to partially solve this problem studying the intersections between the chosen curve and the curves of a given degree (e.g. lines, conics...).
After a brief introduction to the algebraic-geometric codes we will discuss the importance of the determination of the intersections between curves in this context: in particular we will talk about the maximal intersections between the Giulietti-Korchmaros curve and the curves with degree lower or equal to three and the intersections between the norm-trace curve, a natural generalization of the Hermitian curve, and curves of the form y=P(x) where P has degree two or three.

Referenti: Massimiliano Sala, Giancarlo Rinaldo