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 Gilbert-Varshamov bound.

Parent

  • Residue AG code — Every Cartier code is contained in a subfield subcode of a residue AG code.

Child

References

[1]
A. Couvreur, “Codes and the Cartier Operator”, (2012) arXiv:1206.4728
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Zoo Code ID: cartier

Cite as:
“Cartier code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cartier
BibTeX:
@incollection{eczoo_cartier, title={Cartier code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cartier} }
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Permanent link:
https://errorcorrectionzoo.org/c/cartier

Cite as:

“Cartier code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/cartier

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/residueAG/cartier.yml.