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arXiv · 2304.07083

Faster List Decoding of AG Codes

Peter Beelen·Vincent Neiger
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Abstract

In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$ operations in the underlying finite field, where $n$ is the code length, $g$ is the genus of the function field used to construct the code, $s$ is the multiplicity parameter, $\ell$ is the designed list size and $\mu$ is the smallest positive element in the Weierstrass semigroup of some chosen place.

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Peter Beelen, Vincent Neiger. 2023-04-14. Faster List Decoding of AG Codes. https://doi.org/10.1109/tit.2025.3550750

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