{"paper":{"title":"Weight distribution of cyclic codes defined by quadratic forms and related curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Denis E. Videla, Ricardo A. Podest\\'a","submitted_at":"2019-03-05T14:19:20Z","abstract_excerpt":"We consider cyclic codes $\\mathcal{C}_\\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \\operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\\mathcal{L}$ of $q$-linearized polynomials $R$ over $\\mathbb{F}_{q^m}$, and three related codes $\\mathcal{C}_{\\mathcal{L},0}$, $\\mathcal{C}_{\\mathcal{L},1}$ and $\\mathcal{C}_{\\mathcal{L},2}$. We describe the spectra for all these codes when $\\mathcal{L}$ is an even rank family, in terms of the distribution of ranks of the forms $Q_R$ in the family $\\mathcal{L}$, and we also compute the complete weight enumerator for $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01838","kind":"arxiv","version":3},"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/1903.01838/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"}