{"paper":{"title":"Minimum-weight codewords of the Hermitian codes are supported on complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Chiara Marcolla, Margherita Roggero","submitted_at":"2016-05-25T11:11:55Z","abstract_excerpt":"Let $\\mathcal{H}$ be the Hermitian curve defined over a finite field $\\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over $\\mathcal{H}$, started in [1]: if $d$ is the distance of the code, the supports are all the sets of $d$ distinct $\\mathbb{F}_{q^2}$-points on $\\mathcal{H}$ complete intersection of two curves defined by polynomials with prescribed initial monomials w.r.t. \\texttt{DegRevLex}.\n  For most Hermitian codes, and especially for all those with distance $d\\geq q^2-q$ studie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07827","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}