Nonlinear AG code[1][2][3][4][5]

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]
Noam D. Elkies, “Excellent nonlinear codes from modular curves”. 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]
Noam D. Elkies, “Still better nonlinear codes from modular curves”. 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

Zoo code information

Internal code ID: nonlinear_ag

Your contribution is welcome!

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Zoo Code ID: nonlinear_ag

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/nonlinear_ag.yml.