{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TAYKW5H2H3YP5R5COVDIZTBLRQ","short_pith_number":"pith:TAYKW5H2","canonical_record":{"source":{"id":"1601.02328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T05:51:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"800847fbe3eb8ac5ee52d44a9243b16f01318458686910aa4d5eded26eac3eb2","abstract_canon_sha256":"e4286c7607c3a02c02da2cba213d2670242e94d55555990013a036ddc5100bb3"},"schema_version":"1.0"},"canonical_sha256":"9830ab74fa3ef0fec7a275468ccc2b8c30a2265f6c799d307b8b528fea4092bf","source":{"kind":"arxiv","id":"1601.02328","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02328","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02328v2","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02328","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"TAYKW5H2H3YP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TAYKW5H2H3YP5R5C","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TAYKW5H2","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TAYKW5H2H3YP5R5COVDIZTBLRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T05:51:32Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"800847fbe3eb8ac5ee52d44a9243b16f01318458686910aa4d5eded26eac3eb2","abstract_canon_sha256":"e4286c7607c3a02c02da2cba213d2670242e94d55555990013a036ddc5100bb3"},"schema_version":"1.0"},"canonical_sha256":"9830ab74fa3ef0fec7a275468ccc2b8c30a2265f6c799d307b8b528fea4092bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:02.017235Z","signature_b64":"RCld5gFiWcAxhBzsvOeQL/bIwjcue+JwVKb4AsU9ae+6ug25tWK3f9hcE9OU3+/zBX+t5aZwmubQX7w+GHlSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9830ab74fa3ef0fec7a275468ccc2b8c30a2265f6c799d307b8b528fea4092bf","last_reissued_at":"2026-05-18T01:23:02.016557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:02.016557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02328","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSuh3nkEJMycvCdri1mZ6XtnbZf/ztV1odx6NCnkyM3PBe92wHSU3xYFhkaxA1OzyLynpdB7x+d44Zjl6E35Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:12:46.710783Z"},"content_sha256":"427132ff47550a019ee600a4ec4a1ffae01736959e0442e0485782fba0405a1c","schema_version":"1.0","event_id":"sha256:427132ff47550a019ee600a4ec4a1ffae01736959e0442e0485782fba0405a1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TAYKW5H2H3YP5R5COVDIZTBLRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Quantum Codes Obtained From Cyclic Codes Over $\\mathbb{F}_2+u\\mathbb{F}_2+u^2\\mathbb{F}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhay Kumar Singh, Pratyush Kumar, Sukhamoy Pattanayak","submitted_at":"2016-01-11T05:51:32Z","abstract_excerpt":"Let $R=\\mathbb{F}_2+u\\mathbb{F}_2+u^2\\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over $\\mathbb{F}_2$ as gray images of linear and cyclic codes over $R$. The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02328","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":""},"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":"2026-05-18T01:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0O32RpY86LBUtMwF0+zEAPyqFcsBrzs81w3BjoXzMPlYVDXfylKpfiO7V7r6d09Axh31K8A7WgWeY6jxF2vLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:12:46.711131Z"},"content_sha256":"8a74d879551f321092c219328a313143ce6362bbbf278b87873fecd76932b456","schema_version":"1.0","event_id":"sha256:8a74d879551f321092c219328a313143ce6362bbbf278b87873fecd76932b456"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/bundle.json","state_url":"https://pith.science/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/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":"2026-06-24T04:12:46Z","links":{"resolver":"https://pith.science/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ","bundle":"https://pith.science/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/bundle.json","state":"https://pith.science/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAYKW5H2H3YP5R5COVDIZTBLRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TAYKW5H2H3YP5R5COVDIZTBLRQ","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":"e4286c7607c3a02c02da2cba213d2670242e94d55555990013a036ddc5100bb3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T05:51:32Z","title_canon_sha256":"800847fbe3eb8ac5ee52d44a9243b16f01318458686910aa4d5eded26eac3eb2"},"schema_version":"1.0","source":{"id":"1601.02328","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02328","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02328v2","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02328","created_at":"2026-05-18T01:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"TAYKW5H2H3YP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TAYKW5H2H3YP5R5C","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TAYKW5H2","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:8a74d879551f321092c219328a313143ce6362bbbf278b87873fecd76932b456","target":"graph","created_at":"2026-05-18T01:23:02Z","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 $R=\\mathbb{F}_2+u\\mathbb{F}_2+u^2\\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over $\\mathbb{F}_2$ as gray images of linear and cyclic codes over $R$. The parameters of quantum codes which are obtained from cyclic code over $R$ are discussed.","authors_text":"Abhay Kumar Singh, Pratyush Kumar, Sukhamoy Pattanayak","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T05:51:32Z","title":"On Quantum Codes Obtained From Cyclic Codes Over $\\mathbb{F}_2+u\\mathbb{F}_2+u^2\\mathbb{F}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02328","kind":"arxiv","version":2},"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":"sha256:427132ff47550a019ee600a4ec4a1ffae01736959e0442e0485782fba0405a1c","target":"record","created_at":"2026-05-18T01:23:02Z","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":"e4286c7607c3a02c02da2cba213d2670242e94d55555990013a036ddc5100bb3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-11T05:51:32Z","title_canon_sha256":"800847fbe3eb8ac5ee52d44a9243b16f01318458686910aa4d5eded26eac3eb2"},"schema_version":"1.0","source":{"id":"1601.02328","kind":"arxiv","version":2}},"canonical_sha256":"9830ab74fa3ef0fec7a275468ccc2b8c30a2265f6c799d307b8b528fea4092bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9830ab74fa3ef0fec7a275468ccc2b8c30a2265f6c799d307b8b528fea4092bf","first_computed_at":"2026-05-18T01:23:02.016557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:02.016557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RCld5gFiWcAxhBzsvOeQL/bIwjcue+JwVKb4AsU9ae+6ug25tWK3f9hcE9OU3+/zBX+t5aZwmubQX7w+GHlSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:02.017235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02328","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:427132ff47550a019ee600a4ec4a1ffae01736959e0442e0485782fba0405a1c","sha256:8a74d879551f321092c219328a313143ce6362bbbf278b87873fecd76932b456"],"state_sha256":"96b6a58f24554c9b7b52b40851516453deda2134f51bd2cd5021eb24d4948150"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDv5BgRhMx7hPBnPSs6AKvWPbJc894fZdn3JyDvGurJqf36xPF/qBZiKNAEVwoNwwsDwc6C2Cxm3orQIBtmOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:12:46.713156Z","bundle_sha256":"8cca9820776f314a94d03c4f5b30ef8764deb40a5bba66c13854da24dc7e6642"}}