Bounded distance decoding of linear error-correcting codes with Gröbner bases

@article{Bulygin2009BoundedDD,
  title={Bounded distance decoding of linear error-correcting codes with Gr{\"o}bner bases},
  author={Stanislav Bulygin and Ruud Pellikaan},
  journal={J. Symb. Comput.},
  year={2009},
  volume={44},
  pages={1626-1643}
}
The problem of bounded distance decoding of arbitrary linear codes using Grobner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when we want to decode up to half the minimum distance, it has a unique solution even over the algebraic closure of the considered finite field, although field equations are not added. The equations in… CONTINUE READING

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