{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L24TW2VZI6NPNFJTXFSZ3EBNEU","short_pith_number":"pith:L24TW2VZ","canonical_record":{"source":{"id":"1803.00467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-28T00:31:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e46fd6cfb431934ac4c1a74b36078030cd235affb0ab6f3ba84ba4d7db246676","abstract_canon_sha256":"0d0dca41432015047a78e8ca4edc4b4d136b3618eb906b69e6582140eff42c9a"},"schema_version":"1.0"},"canonical_sha256":"5eb93b6ab9479af69533b9659d902d25157a712a3d3c2fc41877aa4ed491f771","source":{"kind":"arxiv","id":"1803.00467","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00467","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00467v1","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00467","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"L24TW2VZI6NP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L24TW2VZI6NPNFJT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L24TW2VZ","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L24TW2VZI6NPNFJTXFSZ3EBNEU","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-28T00:31:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e46fd6cfb431934ac4c1a74b36078030cd235affb0ab6f3ba84ba4d7db246676","abstract_canon_sha256":"0d0dca41432015047a78e8ca4edc4b4d136b3618eb906b69e6582140eff42c9a"},"schema_version":"1.0"},"canonical_sha256":"5eb93b6ab9479af69533b9659d902d25157a712a3d3c2fc41877aa4ed491f771","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:11.672031Z","signature_b64":"l/ERgGuFXgFXqM8jgMtLiHfmQAxTJK9qU5HQvrkRN/CvGu+Xt2XqeHCpKeRqUbWDkLjiHl7MKkMER9cJEuB7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eb93b6ab9479af69533b9659d902d25157a712a3d3c2fc41877aa4ed491f771","last_reissued_at":"2026-05-18T00:22:11.671397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:11.671397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00467","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6Za9gbA5tmX14gFYVetfrARCY4sLkHVRMBKNfQe4wOMm3TfcoxUCd27R0CcyjmfarVlIg7cU8TA7jgRSpcvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:31:19.337986Z"},"content_sha256":"e154912ba7496e0110381a34c6cc10879845da495db8e2f6dcc617aa8306204b","schema_version":"1.0","event_id":"sha256:e154912ba7496e0110381a34c6cc10879845da495db8e2f6dcc617aa8306204b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L24TW2VZI6NPNFJTXFSZ3EBNEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Negacyclic codes over the local ring $\\mathbb{Z}_4[v]/\\langle v^2+2v\\rangle$ of oddly even length and their Gray images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Yonglin Cao, Yuan Cao","submitted_at":"2018-02-28T00:31:22Z","abstract_excerpt":"Let $R=\\mathbb{Z}_{4}[v]/\\langle v^2+2v\\rangle=\\mathbb{Z}_{4}+v\\mathbb{Z}_{4}$ ($v^2=2v$) and $n$ be an odd positive integer. Then $R$ is a local non-principal ideal ring of $16$ elements and there is a $\\mathbb{Z}_{4}$-linear Gray map from $R$ onto $\\mathbb{Z}_{4}^2$ which preserves Lee distance and orthogonality. First, a canonical form decomposition and the structure for any negacyclic code over $R$ of length $2n$ are presented. From this decomposition, a complete classification of all these codes is obtained. Then the cardinality and the dual code for each of these codes are given, and sel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00467","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bvCvztWonOc8Mj6XjZnvZ25Zx0P1bOvuS72wz/XIk3HE9UZvRrz27/zZDyi5pw8ScH0gH6tv6RxYrMaE8drWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:31:19.338356Z"},"content_sha256":"3fcb4bc95c5b2ed8e19e989ba20b68a77cc7c9358ddbc53cc128cbfebcfd92dd","schema_version":"1.0","event_id":"sha256:3fcb4bc95c5b2ed8e19e989ba20b68a77cc7c9358ddbc53cc128cbfebcfd92dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/bundle.json","state_url":"https://pith.science/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T11:31:19Z","links":{"resolver":"https://pith.science/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU","bundle":"https://pith.science/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/bundle.json","state":"https://pith.science/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L24TW2VZI6NPNFJTXFSZ3EBNEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L24TW2VZI6NPNFJTXFSZ3EBNEU","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":"0d0dca41432015047a78e8ca4edc4b4d136b3618eb906b69e6582140eff42c9a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-28T00:31:22Z","title_canon_sha256":"e46fd6cfb431934ac4c1a74b36078030cd235affb0ab6f3ba84ba4d7db246676"},"schema_version":"1.0","source":{"id":"1803.00467","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00467","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00467v1","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00467","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"L24TW2VZI6NP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L24TW2VZI6NPNFJT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L24TW2VZ","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:3fcb4bc95c5b2ed8e19e989ba20b68a77cc7c9358ddbc53cc128cbfebcfd92dd","target":"graph","created_at":"2026-05-18T00:22:11Z","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 $R=\\mathbb{Z}_{4}[v]/\\langle v^2+2v\\rangle=\\mathbb{Z}_{4}+v\\mathbb{Z}_{4}$ ($v^2=2v$) and $n$ be an odd positive integer. Then $R$ is a local non-principal ideal ring of $16$ elements and there is a $\\mathbb{Z}_{4}$-linear Gray map from $R$ onto $\\mathbb{Z}_{4}^2$ which preserves Lee distance and orthogonality. First, a canonical form decomposition and the structure for any negacyclic code over $R$ of length $2n$ are presented. From this decomposition, a complete classification of all these codes is obtained. Then the cardinality and the dual code for each of these codes are given, and sel","authors_text":"Yonglin Cao, Yuan Cao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-28T00:31:22Z","title":"Negacyclic codes over the local ring $\\mathbb{Z}_4[v]/\\langle v^2+2v\\rangle$ of oddly even length and their Gray images"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00467","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:e154912ba7496e0110381a34c6cc10879845da495db8e2f6dcc617aa8306204b","target":"record","created_at":"2026-05-18T00:22:11Z","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":"0d0dca41432015047a78e8ca4edc4b4d136b3618eb906b69e6582140eff42c9a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-28T00:31:22Z","title_canon_sha256":"e46fd6cfb431934ac4c1a74b36078030cd235affb0ab6f3ba84ba4d7db246676"},"schema_version":"1.0","source":{"id":"1803.00467","kind":"arxiv","version":1}},"canonical_sha256":"5eb93b6ab9479af69533b9659d902d25157a712a3d3c2fc41877aa4ed491f771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5eb93b6ab9479af69533b9659d902d25157a712a3d3c2fc41877aa4ed491f771","first_computed_at":"2026-05-18T00:22:11.671397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:11.671397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l/ERgGuFXgFXqM8jgMtLiHfmQAxTJK9qU5HQvrkRN/CvGu+Xt2XqeHCpKeRqUbWDkLjiHl7MKkMER9cJEuB7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:11.672031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00467","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e154912ba7496e0110381a34c6cc10879845da495db8e2f6dcc617aa8306204b","sha256:3fcb4bc95c5b2ed8e19e989ba20b68a77cc7c9358ddbc53cc128cbfebcfd92dd"],"state_sha256":"3a8613e6670e3b125793a196f495924fee149f9b6f18e1cc91fcbea328cb1e52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GrkZdC/p40eCy+7gz8phJ1koF9CNjaZELrlpKMp7XJ8aHac4LgEctSvPQxPRcwI8ooA59pWILxV3T7MfK3awCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:31:19.340189Z","bundle_sha256":"fc87357e6a244f1a48ad8cc58145dd2acce4f4ed3b80dc6fee5cadf9572ba855"}}