Decoding Affine Variety Codes Using Gröbner Bases

@article{Fitzgerald1998DecodingAV,
  title={Decoding Affine Variety Codes Using Gr{\"o}bner Bases},
  author={J. Fitzgerald and Robert F. Lax},
  journal={Designs, Codes and Cryptography},
  year={1998},
  volume={13},
  pages={147-158}
}
We define a class of codes that we call affine variety codes. These codes are obtained by evaluating functions in the coordinate ring of an affine variety on all the Fq-rational points of the variety. We show that one can, at least in theory, decode these codes up to half the true minimum distance by using the theory of Gröbner bases. We extend results of A. B. Cooper and of X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong. 

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