Cartier code[1]
Description
A generalization of the Goppa codes to codes defined from curves of non-zero genus. Each code is a subcode of a certain residue AG code and is constructed using the Cartier operator.
Rate
Cartier codes share similar asymptotic properties as subfield subcodes of residue AG codes, with both families admitting sequences of codes that achieve the GV bound.
Parents
Child
- Classical Goppa code — Goppa codes are Cartier codes from a curve of genus zero [1].
Cousin
- Residue AG code — Every Cartier code is contained in a subfield subcode of a residue AG code. Cartier codes share similar asymptotic properties as subfield subcodes of residue AG codes, with both families admitting sequences of codes that achieve the GV bound.
References
- [1]
- A. Couvreur, “Codes and the Cartier Operator”, (2012) arXiv:1206.4728
Page edit log
- Victor V. Albert (2022-08-04) — most recent
Cite as:
“Cartier code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cartier