{"paper":{"title":"Weights which respect support and NN-decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Marcelo Firer, Roberto Assis Machado","submitted_at":"2018-04-20T19:57:36Z","abstract_excerpt":"In this work we explore a family of metrics over finite fields which respect the support of vectors. We show how these metrics can be obtained from the edge-weighted Hamming cube and, based on this representation we give a description of a group of linear isometries (with respect to the metric). Next we introduce the concept of conditional sum of metrics and determine what conditions determine a metric respecting support, out of two such given metrics. Finally we introduce the labeled-poset block metrics, a new family of metrics which respects support of vector, filling a gap existing in the k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07809","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"}