Sub-quadratic Decoding of One-point Hermitian Codes
arXiv:1405.6008 · doi:10.1109/TIT.2015.2424415
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.
New version includes simulation results, improves some complexity results, as well as a number of reviewer corrections. 20 pages