{"paper":{"title":"On a condition equivalent to the Maximum Distance Separable conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Daniel Kaiser, Jeffery Sun, Steven Damelin","submitted_at":"2016-11-08T01:10:35Z","abstract_excerpt":"We denote by $\\mathcal{P}_q$ the vector space of functions from a finite field $\\mathbb{F}_q$ to itself, which can be represented as the space $\\mathcal{P}_q := \\mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\\mathcal{O}_n \\subset \\mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\\mathcal{P}_q$, we denote by $\\langle Y,Z \\rangle$ their span. We prove that the following are equivalent.\n  A) Let $k, q$ integers, with $q$ a prime power and $2 \\leq k \\leq q$. Suppose that ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02354","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":""},"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"}