{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2IYLVI46M4YQLNWLWQUJ3RCMCB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"78c62cdd7a20f1abfb41374a775e753febe7ae27eae0eec55bdae1746b3e94d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-10T14:54:21Z","title_canon_sha256":"5b00e18666d4b4393b44bb5f0b5573437da3d8bcc57a2408accd14154cc2c88e"},"schema_version":"1.0","source":{"id":"1503.02939","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02939","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02939v1","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02939","created_at":"2026-05-18T02:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"2IYLVI46M4YQ","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2IYLVI46M4YQLNWL","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2IYLVI46","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f4626c5e44a6a0f5f43f2e360f960603d02a887e12f987dec80a31bb80654a9e","target":"graph","created_at":"2026-05-18T02:25:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from \\$\\alpha\\$-circulant matrices. For a non-trivial ideal I<R we give a method to lift such codes over R/I to codes over R, such that some isomorphic copies are avoided.\n  For the case where I is the minimal ideal of a finite chain ring we refine this lifting method: We impose the additional restriction that lifting preserves self-duality. It will be shown that this can be achieved by solving a linear system of equations over a finite field.\n  Finally we apply this technique to Z_4-linear d","authors_text":"Alfred Wassermann, Michael Kiermaier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-10T14:54:21Z","title":"Double and bordered \\$\\alpha\\$-circulant self-dual codes over finite commutative chain rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02939","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5570ab64c9253bf94d206d6d0252f801de23aa1d8a3c71e293ed585f44969685","target":"record","created_at":"2026-05-18T02:25:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"78c62cdd7a20f1abfb41374a775e753febe7ae27eae0eec55bdae1746b3e94d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-10T14:54:21Z","title_canon_sha256":"5b00e18666d4b4393b44bb5f0b5573437da3d8bcc57a2408accd14154cc2c88e"},"schema_version":"1.0","source":{"id":"1503.02939","kind":"arxiv","version":1}},"canonical_sha256":"d230baa39e673105b6cbb4289dc44c107ad2ddc159aa40bce7e99265e1b70aaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d230baa39e673105b6cbb4289dc44c107ad2ddc159aa40bce7e99265e1b70aaa","first_computed_at":"2026-05-18T02:25:12.703873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:12.703873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H5V16UL8zgv1O8KPgzQ2QfUy3BjGWCqHlQ2ZAmsAvYxITWA5oifpyxU56pvMrYlj+ilTNLgDxDT4Ok6DhHNgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:12.704398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02939","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5570ab64c9253bf94d206d6d0252f801de23aa1d8a3c71e293ed585f44969685","sha256:f4626c5e44a6a0f5f43f2e360f960603d02a887e12f987dec80a31bb80654a9e"],"state_sha256":"f74b7b80348478ee3422cee66e593103258210112aa1ba9ad470b0fabcc8c064"}