Description
Nonlinear \(q\)-ary code constructed by evaluating functions on an algebraic curve.
Rate
Certain nonlinear code sequences beat the Tsfasman-Vladut-Zink bound, outperforming linear AG codes.
Parent
References
- [1]
- N. D. Elkies, “Excellent nonlinear codes from modular curves”, (2001) arXiv:math/0104115
- [2]
- Chaoping Xing, “Nonlinear codes from algebraic curves improving the Tsfasman-Vladut-Zink bound”, IEEE Transactions on Information Theory 49, 1653 (2003) DOI
- [3]
- N. D. Elkies, “Still better nonlinear codes from modular curves”, (2003) arXiv:math/0308046
- [4]
- H. Niederreiter and F. Özbudak, “Constructive Asymptotic Codes with an Improvement on the Tsfasman-Vlăduţ-Zink and Xing Bounds”, Coding, Cryptography and Combinatorics 259 (2004) DOI
- [5]
- H. Stichtenoth and C. Xing, “Excellent Nonlinear Codes From Algebraic Function Fields”, IEEE Transactions on Information Theory 51, 4044 (2005) DOI
Page edit log
- Victor V. Albert (2022-08-04) — most recent
Cite as:
“Nonlinear AG code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/nonlinear_ag