Plane-curve code[1] 


Evaluation AG code of bivariate polynomials of some finite maximum degree, evaluated at points lying on an affine plane curve.


Bezout's theorem yields parameters \([n,k,d]\), which depend on the polynomial used to define the plane curve as well as the maximum degree of the polynomials used for evaluation ([2], pg. 883). Distance bounds can be derived from how the plane curve is embedded in the ambient projective space ([3], Thm. 4.1).


Generalization of the Peterson algorithm for BCH codes [1].


  • Evaluation AG code — Plane-curve codes are evaluation AG codes of bivariate polynomials with \(\cal X\) being an affine plane curve ([2], Thm. 2.27).


J. Justesen et al., “Construction and decoding of a class of algebraic geometry codes”, IEEE Transactions on Information Theory 35, 811 (1989) DOI
T. Høholdt, J.H. Van Lint, and R. Pellikaan, 1998. Algebraic geometry codes. Handbook of coding theory, 1 (Part 1), pp.871-961.
A. Couvreur, “The dual minimum distance of arbitrary-dimensional algebraic–geometric codes”, Journal of Algebra 350, 84 (2012) arXiv:0905.2345 DOI
Page edit log

Your contribution is welcome!

on (edit & pull request)

edit on this site

Zoo Code ID: plane_curve

Cite as:
“Plane-curve code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
  title={Plane-curve code},
  booktitle={The Error Correction Zoo},
  editor={Albert, Victor V. and Faist, Philippe},
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:

Cite as:

“Plane-curve code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.