Algebraic curves and their applications to Coding Theory

• Grant number: 22/16369-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2023
• End date: July 18, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ethan Guy Cotterill
• Grantee: Erik Antonio Rojas Mendoza
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM

Abstract

Since the construction of Algebraic Geometry Codes given by V. D. Goppa in 1977, several objects of Algebraic Geometry have been intensively studied to obtain new constructions of Error Correcting Codes, as well as for to obtain Algebraic Geometry Codes with good properties.In this direction, the research project entitled "Algebraic curves and their applications to Coding Theory" has as its main objective to study the different tools provided in the theory of algebraic curves for the construction of Error Correcting Codes with good parameters. More specifically, the proposed project prioritizes research on the following topics:1. Algebraic curves with many rational points.2. Weierstrass semigroups.3. New constructions of codes via algebraic curves.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

CASTELLANOS, ALONSO S.; MENDOZA, ERIK A. R.; TIZZIOTTI, GUILHERME. Complete set of pure gaps in function fields. Journal of Pure and Applied Algebra, v. 228, n. 4, p. 20-pg., 2024-04-01. (22/16369-2)

S. CASTELLANOS, ALONSO; MENDOZA, ERIK A. R.; TIZZIOTTI, GUILHERME. The set of pure gaps at several rational places in function fields. DESIGNS CODES AND CRYPTOGRAPHY, v. N/A, p. 26-pg., 2024-12-28. (22/16369-2)