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Sub-quadratic Decoding of One-point Hermitian Codes
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 matrix minimisation algorithms from computer algebra, yielding similar asymptotic complexities.
Cited literature [34 references]
https://hal.inria.fr/hal-01245062
Contributor : Johan S. R. Nielsen <>
Submitted on : Thursday, December 17, 2015 - 3:39:26 PM
Last modification on : Friday, April 30, 2021 - 9:56:53 AM
Long-term archiving on: : Saturday, April 29, 2017 - 4:58:56 PM
Contributor : Johan S. R. Nielsen <>
Submitted on : Thursday, December 17, 2015 - 3:39:26 PM
Last modification on : Friday, April 30, 2021 - 9:56:53 AM
Long-term archiving on: : Saturday, April 29, 2017 - 4:58:56 PM
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2015_ieee_hermitian.pdf
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