{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:DXD7CSUBETCCEGX6QVKHQ37BDX","short_pith_number":"pith:DXD7CSUB","schema_version":"1.0","canonical_sha256":"1dc7f14a8124c4221afe8554786fe11de8d2141d527adbe91dc3f57fe158130b","source":{"kind":"arxiv","id":"2210.06241","version":1},"attestation_state":"computed","paper":{"title":"Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Jon-Lark Kim, Minjia Shi, Shitao Li","submitted_at":"2022-10-12T14:27:23Z","abstract_excerpt":"The purpose of this paper is to solve the two conjectures on the largest minimum distance $d_{so}(n,5)$ of a binary self-orthogonal $[n,5]$ code proposed by Kim and Choi (IEEE Trans. Inf. Theory, 2022). The determination of $d_{so}(n,k)$ has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension $k$ increases. Recently, Kim et al. (2021) considered the shortest self-orthogonal embedding of a binary linear code, and many binary optimal self-orthogonal $[n,k]$ codes were constructed for $k=4,5$. Kim and Choi (2022) impro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.06241","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.IT","submitted_at":"2022-10-12T14:27:23Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"b594d9d4f8e97228127ca381c0ca7d6c0ff5db782e5e05e16379ab52b1ac4682","abstract_canon_sha256":"a7bc853d9aa6abaf44dcb9a3798643a3ab8d337e4a1b759a8c44ca58a15740ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:05:58.099410Z","signature_b64":"O9Sb6SnInowVL440uSHzssmMZpP0HEEUV2kWmusXEBUik1iG3eL2lcQxO9EX05CbhWMFbKY6WR3tI+UafgIoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dc7f14a8124c4221afe8554786fe11de8d2141d527adbe91dc3f57fe158130b","last_reissued_at":"2026-07-05T05:05:58.098987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:05:58.098987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Jon-Lark Kim, Minjia Shi, Shitao Li","submitted_at":"2022-10-12T14:27:23Z","abstract_excerpt":"The purpose of this paper is to solve the two conjectures on the largest minimum distance $d_{so}(n,5)$ of a binary self-orthogonal $[n,5]$ code proposed by Kim and Choi (IEEE Trans. Inf. Theory, 2022). The determination of $d_{so}(n,k)$ has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension $k$ increases. Recently, Kim et al. (2021) considered the shortest self-orthogonal embedding of a binary linear code, and many binary optimal self-orthogonal $[n,k]$ codes were constructed for $k=4,5$. Kim and Choi (2022) impro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06241","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.06241/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2210.06241","created_at":"2026-07-05T05:05:58.099046+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.06241v1","created_at":"2026-07-05T05:05:58.099046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06241","created_at":"2026-07-05T05:05:58.099046+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXD7CSUBETCC","created_at":"2026-07-05T05:05:58.099046+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXD7CSUBETCCEGX6","created_at":"2026-07-05T05:05:58.099046+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXD7CSUB","created_at":"2026-07-05T05:05:58.099046+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX","json":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX.json","graph_json":"https://pith.science/api/pith-number/DXD7CSUBETCCEGX6QVKHQ37BDX/graph.json","events_json":"https://pith.science/api/pith-number/DXD7CSUBETCCEGX6QVKHQ37BDX/events.json","paper":"https://pith.science/paper/DXD7CSUB"},"agent_actions":{"view_html":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX","download_json":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX.json","view_paper":"https://pith.science/paper/DXD7CSUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.06241&json=true","fetch_graph":"https://pith.science/api/pith-number/DXD7CSUBETCCEGX6QVKHQ37BDX/graph.json","fetch_events":"https://pith.science/api/pith-number/DXD7CSUBETCCEGX6QVKHQ37BDX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX/action/storage_attestation","attest_author":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX/action/author_attestation","sign_citation":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX/action/citation_signature","submit_replication":"https://pith.science/pith/DXD7CSUBETCCEGX6QVKHQ37BDX/action/replication_record"}},"created_at":"2026-07-05T05:05:58.099046+00:00","updated_at":"2026-07-05T05:05:58.099046+00:00"}