{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SM7L7YT6VC6ILBZEITBUVPLO7Y","short_pith_number":"pith:SM7L7YT6","schema_version":"1.0","canonical_sha256":"933ebfe27ea8bc85872444c34abd6efe10e3f11ab5ede2be3c65f150909d28a3","source":{"kind":"arxiv","id":"1703.05303","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.05303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-14T22:25:18Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"b840ff8d28ad44ebae3fc26854e129593d6120724d52504e07dbd83fef3bed6e","abstract_canon_sha256":"3f7ebb3812628066854ca78a973d3e58394561db47d91580c06f9252dd4fef71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:34.637277Z","signature_b64":"00gA3YTbcpSQHE5HMvez4ApQ2NXTnbez/mWxMEn+zbEuz+9cZLvjMKwULgJCdngYWqv8CLZr44mA9vH1+eFxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"933ebfe27ea8bc85872444c34abd6efe10e3f11ab5ede2be3c65f150909d28a3","last_reissued_at":"2026-05-18T00:48:34.636677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:34.636677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.05303","created_at":"2026-05-18T00:48:34.636753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.05303v1","created_at":"2026-05-18T00:48:34.636753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05303","created_at":"2026-05-18T00:48:34.636753+00:00"},{"alias_kind":"pith_short_12","alias_value":"SM7L7YT6VC6I","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SM7L7YT6VC6ILBZE","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SM7L7YT6","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y","json":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y.json","graph_json":"https://pith.science/api/pith-number/SM7L7YT6VC6ILBZEITBUVPLO7Y/graph.json","events_json":"https://pith.science/api/pith-number/SM7L7YT6VC6ILBZEITBUVPLO7Y/events.json","paper":"https://pith.science/paper/SM7L7YT6"},"agent_actions":{"view_html":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y","download_json":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y.json","view_paper":"https://pith.science/paper/SM7L7YT6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.05303&json=true","fetch_graph":"https://pith.science/api/pith-number/SM7L7YT6VC6ILBZEITBUVPLO7Y/graph.json","fetch_events":"https://pith.science/api/pith-number/SM7L7YT6VC6ILBZEITBUVPLO7Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y/action/storage_attestation","attest_author":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y/action/author_attestation","sign_citation":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y/action/citation_signature","submit_replication":"https://pith.science/pith/SM7L7YT6VC6ILBZEITBUVPLO7Y/action/replication_record"}},"created_at":"2026-05-18T00:48:34.636753+00:00","updated_at":"2026-05-18T00:48:34.636753+00:00"}