{"paper":{"title":"Recursive decoding of Reed-Muller codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ilya Dumer","submitted_at":"2017-03-14T22:25:18Z","abstract_excerpt":"New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\\left\\{\\genfrac{}{}{0pt}{}{m}{r}\\right\\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code $\\left\\{\\genfrac{}{}{0pt}{}{m}{r}\\right\\} $ onto subblocks $u\\in\\left\\{\\genfrac{}{}{0pt}{}{m-1}{r}\\right\\} $ and $v\\in\\left\\{\\genfrac{}{}{0pt}{}{m-1}{r-1}\\right\\} .$ In decoding, we first try to find a subblock $v$ from the better protected code and then proceed with the block $u$. The likelihoods of the received symbols are recalculated in a way similar to belie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05303","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"}