Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910304456146944 |
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| author | Portela, Daniel Camazón Ramos, Juan Antonio López |
| author_facet | Portela, Daniel Camazón Ramos, Juan Antonio López |
| contents | The aim of this article is to give lower bounds on the parameters of algebraic geometric error-correcting codes constructed from projective bundles over Deligne--Lusztig surfaces. The methods based on an intensive use of the intersection theory allow us to extend the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. General bounds are obtained for the case of projective bundles of rank $2$ over standard Deligne-Lusztig surfaces, and some explicit examples coming from surfaces of type $A_{2}$ and ${}^{2}A_{4}$ are given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_11433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties Portela, Daniel Camazón Ramos, Juan Antonio López Information Theory Algebraic Geometry 94B27, 14G50, 14C17, 14L35 The aim of this article is to give lower bounds on the parameters of algebraic geometric error-correcting codes constructed from projective bundles over Deligne--Lusztig surfaces. The methods based on an intensive use of the intersection theory allow us to extend the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. General bounds are obtained for the case of projective bundles of rank $2$ over standard Deligne-Lusztig surfaces, and some explicit examples coming from surfaces of type $A_{2}$ and ${}^{2}A_{4}$ are given. |
| title | Error-Correcting Codes on Projective Bundles over Deligne-Lusztig varieties |
| topic | Information Theory Algebraic Geometry 94B27, 14G50, 14C17, 14L35 |
| url | https://arxiv.org/abs/2401.11433 |