{"paper":{"title":"A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2023-04-05T15:31:55Z","abstract_excerpt":"Reed-Muller codes were introduced in 1954, with a simple explicit construction based on polynomial evaluations, and have long been conjectured to achieve Shannon capacity on symmetric channels. Major progress was made towards a proof over the last decades; using combinatorial weight enumerator bounds, a breakthrough on the erasure channel from sharp thresholds, hypercontractivity arguments, and polarization theory. Another major progress recently established that the bit error probability vanishes slowly below capacity. However, when channels allow for errors, the results of Bourgain-Kalai do "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.02509","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.02509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}