Codes from Goppa codes
| Autor: | Liu, Chunlei |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: The artical is reorganized |
| Databáze: | arXiv |
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