Algebraic Geometry codes in the sum-rank metric
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914815705874432 |
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| author | Berardini, Elena Caruso, Xavier |
| author_facet | Berardini, Elena Caruso, Xavier |
| contents | We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study the parameters of these codes and give lower bounds for their dimension and minimum distance. Our codes exhibit quite good parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry codes in the Hamming metric. Furthermore, our construction yields codes asymptotically better than the sum-rank version of the Gilbert-Varshamov bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08903 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic Geometry codes in the sum-rank metric Berardini, Elena Caruso, Xavier Algebraic Geometry Information Theory We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study the parameters of these codes and give lower bounds for their dimension and minimum distance. Our codes exhibit quite good parameters, respecting a similar bound to Goppa's bound for Algebraic Geometry codes in the Hamming metric. Furthermore, our construction yields codes asymptotically better than the sum-rank version of the Gilbert-Varshamov bound. |
| title | Algebraic Geometry codes in the sum-rank metric |
| topic | Algebraic Geometry Information Theory |
| url | https://arxiv.org/abs/2303.08903 |