{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VQGMY7WAHEOQBGLZL6OWIFZPX7","short_pith_number":"pith:VQGMY7WA","schema_version":"1.0","canonical_sha256":"ac0ccc7ec0391d0099795f9d64172fbff48a0f5a1383f43aec8c703bae65e3a5","source":{"kind":"arxiv","id":"2205.04153","version":2},"attestation_state":"computed","paper":{"title":"Linear Runlength-Limited Subcodes of Reed-Muller Codes and Coding Schemes for Input-Constrained BMS Channels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Navin Kashyap, V. Arvind Rameshwar","submitted_at":"2022-05-09T10:04:17Z","abstract_excerpt":"In this work, we address the question of the largest rate of linear subcodes of Reed-Muller (RM) codes, all of whose codewords respect a runlength-limited (RLL) constraint. Our interest is in the $(d,\\infty)$-RLL constraint, which mandates that every pair of successive $1$s be separated by at least $d$ $0$s. Consider any sequence $\\{{\\mathcal{C}_m}\\}_{m\\geq 1}$ of RM codes with increasing blocklength, whose rates approach $R$, in the limit as the blocklength goes to infinity. We show that for any linear $(d,\\infty)$-RLL subcode, $\\hat{\\mathcal{C}}_m$, of the code $\\mathcal{C}_m$, it holds that"},"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":"2205.04153","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2022-05-09T10:04:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"4326f8a882a3c7020226ca6c9b24b9029e71095199474da3c0c66639b41d5317","abstract_canon_sha256":"89bb280a1742e6a145fd219a99c879d5a54ba5d9c977e202be43baf81d66ac23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:59.526337Z","signature_b64":"gBdQuvGyn73hFHzUcH8/k1TCWoegAOfUnMJsI4eKylGbHU+ItMnbivqgdhTM4BcueIA+tUiQ9atzzPtIT/sFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac0ccc7ec0391d0099795f9d64172fbff48a0f5a1383f43aec8c703bae65e3a5","last_reissued_at":"2026-07-05T04:45:59.525816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:59.525816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Runlength-Limited Subcodes of Reed-Muller Codes and Coding Schemes for Input-Constrained BMS Channels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Navin Kashyap, V. Arvind Rameshwar","submitted_at":"2022-05-09T10:04:17Z","abstract_excerpt":"In this work, we address the question of the largest rate of linear subcodes of Reed-Muller (RM) codes, all of whose codewords respect a runlength-limited (RLL) constraint. Our interest is in the $(d,\\infty)$-RLL constraint, which mandates that every pair of successive $1$s be separated by at least $d$ $0$s. Consider any sequence $\\{{\\mathcal{C}_m}\\}_{m\\geq 1}$ of RM codes with increasing blocklength, whose rates approach $R$, in the limit as the blocklength goes to infinity. We show that for any linear $(d,\\infty)$-RLL subcode, $\\hat{\\mathcal{C}}_m$, of the code $\\mathcal{C}_m$, it holds that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.04153","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.04153/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.04153","created_at":"2026-07-05T04:45:59.525894+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.04153v2","created_at":"2026-07-05T04:45:59.525894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.04153","created_at":"2026-07-05T04:45:59.525894+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQGMY7WAHEOQ","created_at":"2026-07-05T04:45:59.525894+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQGMY7WAHEOQBGLZ","created_at":"2026-07-05T04:45:59.525894+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQGMY7WA","created_at":"2026-07-05T04:45:59.525894+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/VQGMY7WAHEOQBGLZL6OWIFZPX7","json":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7.json","graph_json":"https://pith.science/api/pith-number/VQGMY7WAHEOQBGLZL6OWIFZPX7/graph.json","events_json":"https://pith.science/api/pith-number/VQGMY7WAHEOQBGLZL6OWIFZPX7/events.json","paper":"https://pith.science/paper/VQGMY7WA"},"agent_actions":{"view_html":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7","download_json":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7.json","view_paper":"https://pith.science/paper/VQGMY7WA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.04153&json=true","fetch_graph":"https://pith.science/api/pith-number/VQGMY7WAHEOQBGLZL6OWIFZPX7/graph.json","fetch_events":"https://pith.science/api/pith-number/VQGMY7WAHEOQBGLZL6OWIFZPX7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7/action/storage_attestation","attest_author":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7/action/author_attestation","sign_citation":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7/action/citation_signature","submit_replication":"https://pith.science/pith/VQGMY7WAHEOQBGLZL6OWIFZPX7/action/replication_record"}},"created_at":"2026-07-05T04:45:59.525894+00:00","updated_at":"2026-07-05T04:45:59.525894+00:00"}