Improved power decoding of interleaved one-point Hermitian codes

Abstract

An $$h$$ -interleaved one-point Hermitian code is a direct sum of $$h$$ many one-point Hermitian codes, where errors are assumed to occur at the same positions in the constituent codewords. We propose a new partial decoding algorithm for these codes that can decode—under certain assumptions—an error of relative weight up to $$1-\big (\tfrac{k+g}{n}\big )^{\frac{h}{h+1}}$$ , 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 improved power decoding to interleaved Reed–Solomon codes, does not require an expensive root-finding step, and improves upon the previous best decoding radius 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.