Fast Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces

@article{Nakashima2016FastDO,
  title={Fast Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces},
  author={Norihiro Nakashima and Hajime Matsui},
  journal={IEICE Transactions},
  year={2016},
  volume={99-A},
  pages={733-741}
}
A projective Reed–Muller (PRM) code, obtained by modifying a Reed–Muller code with respect to a projective space, is a doubly extended Reed–Sol omon code when the dimension of the related projective space is equal to 1. The minimum distance d the dual code of a PRM code are known, and some decoding examples have been presented for lo w-dimensional projective spaces. In this study, we construct a decoding algorithm for all PRM c odes by dividing a projective space into a union of affine spaces… CONTINUE READING
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