Faster List Decoding of AG Codes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908755783843840 |
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| author | Beelen, Peter Neiger, Vincent |
| author_facet | Beelen, Peter Neiger, Vincent |
| contents | 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 $\tilde{O}(s^2\ell^{ω-1}μ^{ω-1}(n+g) + \ell^ωμ^ω)$ 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 $μ$ is the smallest positive element in the Weierstrass semigroup of some chosen place. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07083 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Faster List Decoding of AG Codes Beelen, Peter Neiger, Vincent Information Theory Symbolic Computation 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 $\tilde{O}(s^2\ell^{ω-1}μ^{ω-1}(n+g) + \ell^ωμ^ω)$ 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 $μ$ is the smallest positive element in the Weierstrass semigroup of some chosen place. |
| title | Faster List Decoding of AG Codes |
| topic | Information Theory Symbolic Computation |
| url | https://arxiv.org/abs/2304.07083 |