Sub-Quadratic Decoding of One-Point Hermitian Codes

  title={Sub-Quadratic Decoding of One-Point Hermitian Codes},
  author={Johan Sebastian Rosenkilde Nielsen and Peter Beelen},
  journal={IEEE Transactions on Information Theory},
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the… 

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