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Journal Articles IEEE Transactions on Information Theory Year : 2015

Sub-quadratic Decoding of One-point Hermitian Codes


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 matrix minimisation algorithms from computer algebra, yielding similar asymptotic complexities.
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hal-01245062 , version 1 (17-12-2015)



Johan Sebastian Rosenkilde Nielsen, Peter Beelen. Sub-quadratic Decoding of One-point Hermitian Codes. IEEE Transactions on Information Theory, 2015, 61 (6), pp.3225-3240 ⟨10.1109/TIT.2015.2424415⟩. ⟨hal-01245062⟩
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