On the decoding radius of lee-metric decoding of algebraic-geometric codes

Abstract

The theory of algebraic-geometric codes with respect to the Hamming metric has been well developed. However, in many applications where non-binary signals are transmitted or stored the Lee metric is a more appropriate metric than the Hamming metric. In our previous work, we presented a polynomial-time Lee-metric decoding algorithm for algebraic-geometric codes. Our algorithm generalizes the interpolation-based Lee-metric decoding algorithm for Reed-Solomon codes in the literature. In this paper, we derive an explicit upper bound on the Lee-error correcting radius of our decoding algorithm. The bound also applies to the Lee-metric Reed-Solomon decoding. As far as we know no such explicit boun..