{"paper":{"title":"The \"art of trellis decoding\" is fixed-parameter tractable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Eun Jung Kim, Jisu Jeong, Sang-il Oum","submitted_at":"2015-07-08T14:57:05Z","abstract_excerpt":"Given n subspaces of a finite-dimensional vector space over a fixed finite field $\\mathbb F$, we wish to find a linear layout $V_1,V_2,\\ldots,V_n$ of the subspaces such that $\\dim((V_1+V_2+\\cdots+V_i) \\cap (V_{i+1}+\\cdots+V_n))\\le k$ for all i, such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory and computing the path-width of an $\\mathbb F$-represented matroid in matroid theory.\n  We present a fixed-parameter tractable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02184","kind":"arxiv","version":4},"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"}