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Elliptic code

Description

Evaluation AG code of rational functions evaluated on points lying on an elliptic curve, i.e., a curve of genus one.

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Evaluation code
Evaluation AG codeAG ECC
Parents
Evaluation AG code
Elliptic codes are evaluation AG codes with \(\cal X\) being an elliptic curve, i.e., curve of genus one [3,4][2; Ch. 3.2].
Elliptic code

References

[1]
A. Couvreur, H. Randriambololona, "Algebraic Geometry Codes and Some Applications." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[2]
M. A. Tsfasman and S. G. Vlăduţ, Algebraic-Geometric Codes (Springer Netherlands, 1991) DOI
[3]
M. Tsfasman, S. Vlǎduţ, and D. Nogin. Algebraic geometric codes: basic notions. Vol. 139. American Mathematical Society, 2022.
[4]
T. Høholdt, J.H. Van Lint, and R. Pellikaan, 1998. Algebraic geometry codes. Handbook of coding theory, 1 (Part 1), pp.871-961.
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Zoo Code ID: elliptic

Cite as:
“Elliptic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/elliptic
BibTeX:
@incollection{eczoo_elliptic, title={Elliptic code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/elliptic} }
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Permanent link:
https://errorcorrectionzoo.org/c/elliptic

Cite as:

“Elliptic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/elliptic

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