{"paper":{"title":"The conorm code of an AG-code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mar\\'ia Chara, Ricardo A. Podest\\'a, Ricardo Toledano","submitted_at":"2019-10-23T18:19:16Z","abstract_excerpt":"Given a suitable extension $F'/F$ of algebraic function fields over a finite field $\\mathbb{F}_q$, we introduce the conorm code $\\text{Con}_{F'/F}(\\mathcal{C})$ defined over $F'$ which is constructed from an algebraic geometry code $\\mathcal{C}$ defined over $F$. We study the parameters of $\\text{Con}_{F'/F}(\\mathcal{C})$ in terms of the parameters of $\\mathcal{C}$, the ramification behavior of the places used to define $\\mathcal{C}$ and the genus of $F$. In the case of unramified extensions of function fields we prove that $\\text{Con}_{F'/F}(\\mathcal{C})^\\perp = \\text{Con}_{F'/F}({\\mathcal{C}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.10753","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.10753/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}