{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K36TQ7T2EUXWXMOQLK3TLPHVLP","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":"d4cc8e77de806d4b0415b5d18a215244fe7df1db4347bd86273d5660a318b795","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-24T08:00:27Z","title_canon_sha256":"592adfb39d29964c89f51ea2818abd368395f56df181f799c026fd23ee9a90c7"},"schema_version":"1.0","source":{"id":"1506.07273","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07273","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07273v1","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07273","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"K36TQ7T2EUXW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K36TQ7T2EUXWXMOQ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K36TQ7T2","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:6bba1c81726bf9e3cd55509b0a8a06f367740a323f458b12d046187bd7f35de9","target":"graph","created_at":"2026-05-18T01:39:54Z","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":"Let $\\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\\mathbb{F}_p+u\\mathbb{F}_p+u^2\\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind of codes and investigate the structural properties of these codes by a decomposition theorem.","authors_text":"Hojjat Mostafanasab, Negin Karimi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-24T08:00:27Z","title":"$(1-2u^2)$-constacyclic codes over $\\mathbb{F}_p+u\\mathbb{F}_p+u^2\\mathbb{F}_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07273","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:cc55509a65d37ce27a672dd9b92027c6558c56940f44620d5c77a4ac2171004c","target":"record","created_at":"2026-05-18T01:39:54Z","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":"d4cc8e77de806d4b0415b5d18a215244fe7df1db4347bd86273d5660a318b795","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-24T08:00:27Z","title_canon_sha256":"592adfb39d29964c89f51ea2818abd368395f56df181f799c026fd23ee9a90c7"},"schema_version":"1.0","source":{"id":"1506.07273","kind":"arxiv","version":1}},"canonical_sha256":"56fd387e7a252f6bb1d05ab735bcf55beab15797698c28d523bfd4ebfab1c51e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56fd387e7a252f6bb1d05ab735bcf55beab15797698c28d523bfd4ebfab1c51e","first_computed_at":"2026-05-18T01:39:54.419981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:54.419981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4Wqu2Or3LTRMpetCB2vB/f+zcUYIt1oQzJCm2uHClSVg5au6RCn0kcIR7WbPF0M3gWdRXGlEao43j/IQsYBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:54.420514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07273","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc55509a65d37ce27a672dd9b92027c6558c56940f44620d5c77a4ac2171004c","sha256:6bba1c81726bf9e3cd55509b0a8a06f367740a323f458b12d046187bd7f35de9"],"state_sha256":"ae471155321b1494235b63656c01fe3ccd6d0291f91f2e16de5b8064aefd5d6e"}