{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:E46FOAI7RW3J5UCMTXRS4QNGZY","short_pith_number":"pith:E46FOAI7","schema_version":"1.0","canonical_sha256":"273c57011f8db69ed04c9de32e41a6ce1214f279f20711723135cae9a82cd12e","source":{"kind":"arxiv","id":"2606.08964","version":1},"attestation_state":"computed","paper":{"title":"Embedding linear codes over Z4 into self-orthogonal codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jon-Lark Kim, Junmin An, San Ling","submitted_at":"2026-06-08T03:04:08Z","abstract_excerpt":"The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-orthogonal embedding over Z4, and determine the exact shortest self-orthogonal embedding length under specific conditions. As an example satisfying these conditions, we establish the exact length of the shortest self-orthogonal embedding for the quaternary Preparata codes. Furthermore, to establish these results, we completely classify the exact length of the shortest doubly even self-orthogonal embedding for binary linea"},"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":"2606.08964","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-06-08T03:04:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ae66d34c35baae4c42001b5311e3278aa8d58e02372b04fa4b6c3798e5547981","abstract_canon_sha256":"292f9e95abf3293f5b460d9dcb3488d0ecc0be1f3586b8cb56fb7e69a102ed71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:50.566757Z","signature_b64":"A0cLo049DgQGGnU3Wcr/6NhUYCVCDC2RfBk3gE/J+SSk7mVN71qkwYdjoD++mwlr5DFQNVcYcQ3QY4WC2lK6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"273c57011f8db69ed04c9de32e41a6ce1214f279f20711723135cae9a82cd12e","last_reissued_at":"2026-06-09T02:07:50.565877Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:50.565877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding linear codes over Z4 into self-orthogonal codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jon-Lark Kim, Junmin An, San Ling","submitted_at":"2026-06-08T03:04:08Z","abstract_excerpt":"The purpose of this paper is to investigate the self-orthogonal embedding problem for linear codes over Z4. We propose several tight bounds on the length of the shortest self-orthogonal embedding over Z4, and determine the exact shortest self-orthogonal embedding length under specific conditions. As an example satisfying these conditions, we establish the exact length of the shortest self-orthogonal embedding for the quaternary Preparata codes. Furthermore, to establish these results, we completely classify the exact length of the shortest doubly even self-orthogonal embedding for binary linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08964","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/2606.08964/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":"2606.08964","created_at":"2026-06-09T02:07:50.566031+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08964v1","created_at":"2026-06-09T02:07:50.566031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08964","created_at":"2026-06-09T02:07:50.566031+00:00"},{"alias_kind":"pith_short_12","alias_value":"E46FOAI7RW3J","created_at":"2026-06-09T02:07:50.566031+00:00"},{"alias_kind":"pith_short_16","alias_value":"E46FOAI7RW3J5UCM","created_at":"2026-06-09T02:07:50.566031+00:00"},{"alias_kind":"pith_short_8","alias_value":"E46FOAI7","created_at":"2026-06-09T02:07:50.566031+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/E46FOAI7RW3J5UCMTXRS4QNGZY","json":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY.json","graph_json":"https://pith.science/api/pith-number/E46FOAI7RW3J5UCMTXRS4QNGZY/graph.json","events_json":"https://pith.science/api/pith-number/E46FOAI7RW3J5UCMTXRS4QNGZY/events.json","paper":"https://pith.science/paper/E46FOAI7"},"agent_actions":{"view_html":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY","download_json":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY.json","view_paper":"https://pith.science/paper/E46FOAI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08964&json=true","fetch_graph":"https://pith.science/api/pith-number/E46FOAI7RW3J5UCMTXRS4QNGZY/graph.json","fetch_events":"https://pith.science/api/pith-number/E46FOAI7RW3J5UCMTXRS4QNGZY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY/action/storage_attestation","attest_author":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY/action/author_attestation","sign_citation":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY/action/citation_signature","submit_replication":"https://pith.science/pith/E46FOAI7RW3J5UCMTXRS4QNGZY/action/replication_record"}},"created_at":"2026-06-09T02:07:50.566031+00:00","updated_at":"2026-06-09T02:07:50.566031+00:00"}