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arXiv · 1801.07006

Improved Power Decoding of Interleaved One-Point Hermitian Codes

Sven Puchinger·Johan Rosenkilde·Irene Bouw
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Abstract

We propose a new partial decoding algorithm for $h$-interleaved one-point Hermitian codes that can decode-under certain assumptions-an error of relative weight up to $1-(\tfrac{k+g}{n})^{\frac{h}{h+1}}$, where $k$ is the dimension, $n$ the length, and $g$ the genus of the code. Simulation results for various parameters indicate that the new decoder achieves this maximal decoding radius with high probability. The algorithm is based on a recent generalization of Rosenkilde's improved power decoder to interleaved Reed-Solomon codes, does not require an expensive root-finding step, and improves upon the previous best decoding radius by Kampf at all rates. In the special case $h=1$, we obtain an adaption of the improved power decoding algorithm to one-point Hermitian codes, which for all simulated parameters achieves a similar observed failure probability as the Guruswami-Sudan decoder above the latter's guaranteed decoding radius.

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Sven Puchinger, Johan Rosenkilde, Irene Bouw. 2018-01-22. Improved Power Decoding of Interleaved One-Point Hermitian Codes. https://arxiv.org/abs/1801.07006

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