{"paper":{"title":"On the distance between linear codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mariusz Kwiatkowski, Mark Pankov","submitted_at":"2015-05-31T11:00:33Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over the finite field consisting of $q$ elements and let $\\Gamma_{k}(V)$ be the Grassmann graph formed by $k$-dimensional subspaces of $V$, $1<k<n-1$. Denote by $\\Gamma(n,k)_{q}$ the restriction of $\\Gamma_{k}(V)$ to the set of all non-degenerate linear $[n,k]_{q}$ codes. We show that for any two codes the distance in $\\Gamma(n,k)_{q}$ coincides with the distance in $\\Gamma_{k}(V)$ only in the case when $n<(q+1)^2+k-2$, i.e. if $n$ is sufficiently large then for some pairs of codes the distances in the graphs $\\Gamma_{k}(V)$ and $\\Gamma(n,k)_{q}$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00215","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":""},"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"}