A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911760856907776 |
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| author | Bernal, José Joaquín Simón, Juan Jacobo |
| author_facet | Bernal, José Joaquín Simón, Juan Jacobo |
| contents | We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding Bernal, José Joaquín Simón, Juan Jacobo Information Theory We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes. |
| title | A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.10527 |