{"paper":{"title":"MacWilliams-type equivalence relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dong Yeol Oh, Hyun Kwang Kim, Jong Yoon Hyun, Soohak Choi","submitted_at":"2012-05-05T01:52:11Z","abstract_excerpt":"Let $\\mathcal{P}$ be a poset on $[n]$, $\\mathcal{I}(\\mathcal{P})$ the set of order ideals of $\\mathcal{P}$ and $E$ an equivalence relation on $\\mathcal{I}(\\mathcal{P})$. The concepts of the dual relation $E^*$ of an equivalence relation $E$, the $E$-weight (resp. $E^*$-weight) distribution of a linear poset code (resp. its dual poset code) and a MacWilliams-type equivalence relation are introduced. We give a characterization for a MacWilliams-type equivalence relation in terms of MacWilliams-type identities for a linear poset code. Three kinds of equivalence relations on $\\mathcal{I}(\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1090","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"}