{"paper":{"title":"Generalized Hamming weights of affine cartesian codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mrinmoy Datta, Peter Beelen","submitted_at":"2017-06-07T10:20:57Z","abstract_excerpt":"In this article, we give the answer to the following question: Given a field $\\mathbb{F}$, finite subsets $A_1,\\dots,A_m$ of $\\mathbb{F}$, and $r$ linearly independent polynomials $f_1,\\dots,f_r \\in \\mathbb{F}[x_1,\\dots,x_m]$ of total degree at most $d$. What is the maximal number of common zeros $f_1,\\dots,f_r$ can have in $A_1 \\times \\cdots \\times A_m$? For $\\mathbb{F}=\\mathbb{F}_q$, the finite field with $q$ elements, answering this question is equivalent to determining the generalized Hamming weights of the so-called affine Cartesian codes. Seen in this light, our work is a generalization "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02114","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"}