Hermitian-Lifted Codes
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866911770257391616 |
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| author | López, Hiram H. Malmskog, Beth Matthews, Gretchen L Piñero-González, Fernando Wootters, Mary |
| author_facet | López, Hiram H. Malmskog, Beth Matthews, Gretchen L Piñero-González, Fernando Wootters, Mary |
| contents | In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the set of $\mathbb{F}_{q^2}$-rational points on the affine curve. The novelty is in terms of the functions to be evaluated; they are a special set of monomials which restrict to low degree polynomials on lines intersected with the Hermitian curve. As a result, the positions corresponding to points on any line through a given point act as a recovery set for the position corresponding to that point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_05558 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hermitian-Lifted Codes López, Hiram H. Malmskog, Beth Matthews, Gretchen L Piñero-González, Fernando Wootters, Mary Information Theory 94B05, 11T71, 94B27 In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the set of $\mathbb{F}_{q^2}$-rational points on the affine curve. The novelty is in terms of the functions to be evaluated; they are a special set of monomials which restrict to low degree polynomials on lines intersected with the Hermitian curve. As a result, the positions corresponding to points on any line through a given point act as a recovery set for the position corresponding to that point. |
| title | Hermitian-Lifted Codes |
| topic | Information Theory 94B05, 11T71, 94B27 |
| url | https://arxiv.org/abs/2006.05558 |