Codes from Goppa codes
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913266924519424 |
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| author | Liu, Chunlei |
| author_facet | Liu, Chunlei |
| contents | On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes approach the Gilbert-Varshamov bound. It is also proved that these codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field, which is usually much small than the location field, where $n$ is the codeword length, and $a$ a constant determined by the polynomial factorization algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19565 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Codes from Goppa codes Liu, Chunlei Information Theory On a Goppa code whose structure polynomial has coefficients in the symbol field, the Frobenius acts. Its fixed codewords form a subcode. Deleting the naturally occurred redundance, we obtain a new code. It is proved that these new codes approach the Gilbert-Varshamov bound. It is also proved that these codes can be decoded within $O(n^2(\logn)^a)$ operations in the symbol field, which is usually much small than the location field, where $n$ is the codeword length, and $a$ a constant determined by the polynomial factorization algorithm. |
| title | Codes from Goppa codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2305.19565 |