{"paper":{"title":"Vanishing ideals over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.AG","math.CO","math.IT"],"primary_cat":"math.AC","authors_text":"Azucena Tochimani, Rafael H. Villarreal","submitted_at":"2015-02-19T00:49:55Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field, let $\\mathbb{X}$ be a subset of a projective space ${\\mathbb P}^{s-1}$, over the field $\\mathbb{F}_q$, parameterized by rational functions, and let $I(\\mathbb{X})$ be the vanishing ideal of $\\mathbb{X}$. The main result of this paper is a formula for $I(\\mathbb{X})$ that will allows us to compute: (i) the algebraic invariants of $I(\\mathbb{X})$, and (ii) the basic parameters of the corresponding Reed-Muller-type code."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05451","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"}