Improved Power Decoding of Interleaved One-Point Hermitian Codes

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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-(k+gn)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.