{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WBKYOZUPUV3DYDMUZB6G2EPD7J","short_pith_number":"pith:WBKYOZUP","canonical_record":{"source":{"id":"2307.08053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-07-16T14:20:12Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0c115487ea0e13ddb845c24dcedbb4a847a85d83e83423d99c3abe16fb531271","abstract_canon_sha256":"86fe6d8753b4214e108dc04a45ae0f75dd8ea86f4a8faebf8fb3c90e2309b7fa"},"schema_version":"1.0"},"canonical_sha256":"b05587668fa5763c0d94c87c6d11e3fa6130b265d7277762270b8c74befc8200","source":{"kind":"arxiv","id":"2307.08053","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.08053","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"2307.08053v2","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08053","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"WBKYOZUPUV3D","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_16","alias_value":"WBKYOZUPUV3DYDMU","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_8","alias_value":"WBKYOZUP","created_at":"2026-07-05T07:19:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WBKYOZUPUV3DYDMUZB6G2EPD7J","target":"record","payload":{"canonical_record":{"source":{"id":"2307.08053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-07-16T14:20:12Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0c115487ea0e13ddb845c24dcedbb4a847a85d83e83423d99c3abe16fb531271","abstract_canon_sha256":"86fe6d8753b4214e108dc04a45ae0f75dd8ea86f4a8faebf8fb3c90e2309b7fa"},"schema_version":"1.0"},"canonical_sha256":"b05587668fa5763c0d94c87c6d11e3fa6130b265d7277762270b8c74befc8200","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:19:20.836163Z","signature_b64":"CPm8pGwl7np6KozAmkGmVOTqdQG3dXa3XDLdYwur0RVxZyUWH+Jm+6j2TBbMtKCu66m3mMXNwhXRAS36caMqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b05587668fa5763c0d94c87c6d11e3fa6130b265d7277762270b8c74befc8200","last_reissued_at":"2026-07-05T07:19:20.835614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:19:20.835614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.08053","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":"2026-07-05T07:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bnvdBEKE9xT338JAXlEhY8fEVRJuGl5aHla8b0Yco8ihiPo22uGVVbYvUiArPsoIlnbldxt9vl4qQR/Xm+UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:19:53.154737Z"},"content_sha256":"5e3dd3858052222be4377851c6c4796261e2906364c2af7e361aeb55e6e22269","schema_version":"1.0","event_id":"sha256:5e3dd3858052222be4377851c6c4796261e2906364c2af7e361aeb55e6e22269"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WBKYOZUPUV3DYDMUZB6G2EPD7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Extended Codes of Some Linear Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Tingfang Chen, Zhonghua Sun","submitted_at":"2023-07-16T14:20:12Z","abstract_excerpt":"The classical way of extending an $[n, k, d]$ linear code $\\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\\C$. This extended code, denoted by $\\overline{\\C}(-\\bone)$ and called the standardly extended code of $\\C$, is a linear code with parameters $[n+1, k, \\bar{d}]$, where $\\bar{d}=d$ or $\\bar{d}=d+1$. This is one of the two extending techniques for linear codes in the literature. The standardly extended codes of some families of binary linear codes have been studied to some extent. However, not much is known about the standardly extended codes of nonbin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.08053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:19:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDUj25pmqulrZ+L9cm/OjGbQHn3InvP5DIomgoFKLiVkEP2lWFHAUuuuTHGleGPyK4tDxFEezRb7LgC0RlcKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:19:53.155750Z"},"content_sha256":"bdb62463fafad7cc6a7a69526ed85d937f20946748463f1fede1dc070e87dc50","schema_version":"1.0","event_id":"sha256:bdb62463fafad7cc6a7a69526ed85d937f20946748463f1fede1dc070e87dc50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/bundle.json","state_url":"https://pith.science/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/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":"2026-07-07T07:19:53Z","links":{"resolver":"https://pith.science/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J","bundle":"https://pith.science/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/bundle.json","state":"https://pith.science/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WBKYOZUPUV3DYDMUZB6G2EPD7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WBKYOZUPUV3DYDMUZB6G2EPD7J","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":"86fe6d8753b4214e108dc04a45ae0f75dd8ea86f4a8faebf8fb3c90e2309b7fa","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-07-16T14:20:12Z","title_canon_sha256":"0c115487ea0e13ddb845c24dcedbb4a847a85d83e83423d99c3abe16fb531271"},"schema_version":"1.0","source":{"id":"2307.08053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.08053","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"2307.08053v2","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08053","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"WBKYOZUPUV3D","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_16","alias_value":"WBKYOZUPUV3DYDMU","created_at":"2026-07-05T07:19:20Z"},{"alias_kind":"pith_short_8","alias_value":"WBKYOZUP","created_at":"2026-07-05T07:19:20Z"}],"graph_snapshots":[{"event_id":"sha256:bdb62463fafad7cc6a7a69526ed85d937f20946748463f1fede1dc070e87dc50","target":"graph","created_at":"2026-07-05T07:19:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.08053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical way of extending an $[n, k, d]$ linear code $\\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\\C$. This extended code, denoted by $\\overline{\\C}(-\\bone)$ and called the standardly extended code of $\\C$, is a linear code with parameters $[n+1, k, \\bar{d}]$, where $\\bar{d}=d$ or $\\bar{d}=d+1$. This is one of the two extending techniques for linear codes in the literature. The standardly extended codes of some families of binary linear codes have been studied to some extent. However, not much is known about the standardly extended codes of nonbin","authors_text":"Cunsheng Ding, Tingfang Chen, Zhonghua Sun","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-07-16T14:20:12Z","title":"The Extended Codes of Some Linear Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08053","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":"sha256:5e3dd3858052222be4377851c6c4796261e2906364c2af7e361aeb55e6e22269","target":"record","created_at":"2026-07-05T07:19:20Z","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":"86fe6d8753b4214e108dc04a45ae0f75dd8ea86f4a8faebf8fb3c90e2309b7fa","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-07-16T14:20:12Z","title_canon_sha256":"0c115487ea0e13ddb845c24dcedbb4a847a85d83e83423d99c3abe16fb531271"},"schema_version":"1.0","source":{"id":"2307.08053","kind":"arxiv","version":2}},"canonical_sha256":"b05587668fa5763c0d94c87c6d11e3fa6130b265d7277762270b8c74befc8200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b05587668fa5763c0d94c87c6d11e3fa6130b265d7277762270b8c74befc8200","first_computed_at":"2026-07-05T07:19:20.835614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:19:20.835614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CPm8pGwl7np6KozAmkGmVOTqdQG3dXa3XDLdYwur0RVxZyUWH+Jm+6j2TBbMtKCu66m3mMXNwhXRAS36caMqDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:19:20.836163Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.08053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3dd3858052222be4377851c6c4796261e2906364c2af7e361aeb55e6e22269","sha256:bdb62463fafad7cc6a7a69526ed85d937f20946748463f1fede1dc070e87dc50"],"state_sha256":"d1921e67e5a34249eaab627d81a6652dc0e2570fd7bca0fcca6ab11a69de5d87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9yEHgGupcG78ic/0Ii8u1cybE2MmKogsttBhtxe4kTozUeoRxORF5D3LTgl/eZjcPZQ4nQMIZnpqbiaez7BCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T07:19:53.159413Z","bundle_sha256":"5565d41ad74d7303d1773807ce1f25e68e89c25319a76425e7cbfcbb2cc4fc2f"}}