Description
Evaluation AG code of rational functions evaluated on points lying on an elliptic curve, i.e., a curve of genus one.
Parent
- Evaluation AG code — Elliptic codes are evaluation AG codes with \(\cal X\) being an elliptic curve, i.e., curve of genus one ([1], Ch. 3.2; [2]).
Cousin
- Maximum distance separable (MDS) code — Elliptic codes can be MDS [3; Ex. 15.5.3][1; pg. 310][4; Sec. 4.4.2].
References
- [1]
- M. A. Tsfasman and S. G. Vlăduţ, Algebraic-Geometric Codes (Springer Netherlands, 1991) DOI
- [2]
- T. Høholdt, J.H. Van Lint, and R. Pellikaan, 1998. Algebraic geometry codes. Handbook of coding theory, 1 (Part 1), pp.871-961.
- [3]
- A. Couvreur, H. Randriambololona, "Algebraic Geometry Codes and Some Applications." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
- [4]
- M. Tsfasman, S. Vlǎduţ, and D. Nogin. Algebraic geometric codes: basic notions. Vol. 139. American Mathematical Society, 2022.
Page edit log
- En-Jui Kuo (2024-03-18) — most recent
- Victor V. Albert (2024-03-18)
- Victor V. Albert (2022-07-20)
Cite as:
“Elliptic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/elliptic