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arXiv · 1405.6008

Sub-quadratic Decoding of One-point Hermitian Codes

Johan S. R. Nielsen·Peter Beelen
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Abstract

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realisation of the Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimisation. 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 same methods from computer algebra, yielding similar asymptotic complexities.

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Johan S. R. Nielsen, Peter Beelen. 2015-05-25. Sub-quadratic Decoding of One-point Hermitian Codes. https://doi.org/10.1109/tit.2015.2424415

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