{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CD6RSW4E4BEMRBFH5MZJL4IOOR","short_pith_number":"pith:CD6RSW4E","schema_version":"1.0","canonical_sha256":"10fd195b84e048c884a7eb3295f10e744beeaffc75e35afbcb9d276e4e1bb580","source":{"kind":"arxiv","id":"1509.05351","version":1},"attestation_state":"computed","paper":{"title":"Triple cyclic codes over $\\mathbb{Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hojjat Mostafanasab","submitted_at":"2015-09-17T18:09:40Z","abstract_excerpt":"Let $r,s,t$ be three positive integers and $\\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\\mathbb{Z}_2$ if the set of coordinates can be partitioned into three parts that any cyclic shift of the coordinates of the parts leaves invariant the code. These codes can be considered as $\\mathbb{Z}_2[x]$-submodules of $\\frac{\\mathbb{Z}_2[x]}{\\langle x^r-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^s-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^t-1\\rangle}$. We give the minimal generating sets of this kind of co"},"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":"1509.05351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-17T18:09:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c466c32dcccaec827526bf1408075e699485ef484bbd0386ccf0a7b9a97fec94","abstract_canon_sha256":"d1c0bc6461c689155dc534737a5dd00a7e7764284b1a976f99353b749bed664c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:44.116369Z","signature_b64":"GeNE8APCLKzIrDy4GXXoC2iFsEYQu9eclUXfJ8MTB4SRFmaUrl+YtlpsNidnOnZbuKMh/3v6UP0AFo1eOZLGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10fd195b84e048c884a7eb3295f10e744beeaffc75e35afbcb9d276e4e1bb580","last_reissued_at":"2026-05-18T01:32:44.115635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:44.115635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Triple cyclic codes over $\\mathbb{Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hojjat Mostafanasab","submitted_at":"2015-09-17T18:09:40Z","abstract_excerpt":"Let $r,s,t$ be three positive integers and $\\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\\mathbb{Z}_2$ if the set of coordinates can be partitioned into three parts that any cyclic shift of the coordinates of the parts leaves invariant the code. These codes can be considered as $\\mathbb{Z}_2[x]$-submodules of $\\frac{\\mathbb{Z}_2[x]}{\\langle x^r-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^s-1\\rangle}\\times\\frac{\\mathbb{Z}_2[x]}{\\langle x^t-1\\rangle}$. We give the minimal generating sets of this kind of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05351","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":"1509.05351","created_at":"2026-05-18T01:32:44.115726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05351v1","created_at":"2026-05-18T01:32:44.115726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05351","created_at":"2026-05-18T01:32:44.115726+00:00"},{"alias_kind":"pith_short_12","alias_value":"CD6RSW4E4BEM","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"CD6RSW4E4BEMRBFH","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"CD6RSW4E","created_at":"2026-05-18T12:29:14.074870+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/CD6RSW4E4BEMRBFH5MZJL4IOOR","json":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR.json","graph_json":"https://pith.science/api/pith-number/CD6RSW4E4BEMRBFH5MZJL4IOOR/graph.json","events_json":"https://pith.science/api/pith-number/CD6RSW4E4BEMRBFH5MZJL4IOOR/events.json","paper":"https://pith.science/paper/CD6RSW4E"},"agent_actions":{"view_html":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR","download_json":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR.json","view_paper":"https://pith.science/paper/CD6RSW4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05351&json=true","fetch_graph":"https://pith.science/api/pith-number/CD6RSW4E4BEMRBFH5MZJL4IOOR/graph.json","fetch_events":"https://pith.science/api/pith-number/CD6RSW4E4BEMRBFH5MZJL4IOOR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR/action/storage_attestation","attest_author":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR/action/author_attestation","sign_citation":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR/action/citation_signature","submit_replication":"https://pith.science/pith/CD6RSW4E4BEMRBFH5MZJL4IOOR/action/replication_record"}},"created_at":"2026-05-18T01:32:44.115726+00:00","updated_at":"2026-05-18T01:32:44.115726+00:00"}