{"paper":{"title":"Functional codes arising from rank $n$ Hermitian varieties and hypersurfaces in low dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Subrata Manna","submitted_at":"2026-05-22T04:31:53Z","abstract_excerpt":"We study the functional code $C_d(\\mathcal{X})$, introduced by G. Lachaud in 1996, in the case where $\\mathcal{X}$ is a rank $n$ degenerate Hermitian variety $P\\mathcal{U}_{n-1}$ in $\\mathbb{P}^n(\\mathbb{F}_{q^2})$ and $d\\leq q$. We establish an upper bound for the maximum number of $\\mathbb{F}_{q^2}$-rational points in the intersection of $P\\mathcal{U}_{n-1}$ with an $\\mathbb{F}_{q^2}$-hypersurface of degree at most $q$ in $\\mathbb{P}^n$. Using this bound, we determine the parameters of the codes $C_d(P\\mathcal{U}_{n-1})$ in the cases $n=2,3,4$. We also characterize the hypersurfaces that cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23221","kind":"arxiv","version":1},"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/2605.23221/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"}