Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases

@article{Saints1995AlgebraicgeometricCA,
  title={Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases},
  author={Keith Saints and Chris Heegard},
  journal={IEEE Trans. Information Theory},
  year={1995},
  volume={41},
  pages={1733-1751}
}
In this paper, it is proved that any algehraicgeometr ic code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are descr ibed by a unified theory of l inear block codes def ined over point sets: algebraic-geometric codes are def ined over the points of an algebraic curve, and an m-dimensional cyclic code is def ined over the points in mdimensional space. The power of the unified theory is in its… CONTINUE READING
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