{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PL3F22TMVIMGF2PVVAQAUPW4MV","short_pith_number":"pith:PL3F22TM","schema_version":"1.0","canonical_sha256":"7af65d6a6caa1862e9f5a8200a3edc655f91175616628e6631ac53c1db7968bf","source":{"kind":"arxiv","id":"1106.2428","version":2},"attestation_state":"computed","paper":{"title":"On the classification of Hermitian self-dual additive codes over GF(9)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"math.CO","authors_text":"Lars Eirik Danielsen","submitted_at":"2011-06-13T12:29:42Z","abstract_excerpt":"Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. Self-dual additive codes over GF(9) have been classified up to length 8, and in this paper we extend the complete classification to codes of length 9 and 10. The classification is obtained by using a new algorithm th"},"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":"1106.2428","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T12:29:42Z","cross_cats_sorted":["cs.IT","math.IT","quant-ph"],"title_canon_sha256":"a20abd4a7fbb867ec8262bf34168b8f52015f62fecbe6e74c01e822e1e3f0b37","abstract_canon_sha256":"33efdb7b96512c5acfebcd2965f56e9d310c5a0b9d99656ba53d3732e4aea781"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:25.891043Z","signature_b64":"RydCZ14zxtZcdjFJ4UisoS3E7O3sXgL9xV7XgxkQ1C+llNL3UacpkrBIgDWZ6rvESESb4LaTjWBhCHm7fB4JCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af65d6a6caa1862e9f5a8200a3edc655f91175616628e6631ac53c1db7968bf","last_reissued_at":"2026-05-18T03:50:25.890176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:25.890176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification of Hermitian self-dual additive codes over GF(9)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","quant-ph"],"primary_cat":"math.CO","authors_text":"Lars Eirik Danielsen","submitted_at":"2011-06-13T12:29:42Z","abstract_excerpt":"Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes have so far received far less interest from coding theorists than self-dual additive codes over GF(4), which correspond to binary quantum codes. Self-dual additive codes over GF(9) have been classified up to length 8, and in this paper we extend the complete classification to codes of length 9 and 10. The classification is obtained by using a new algorithm th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2428","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1106.2428","created_at":"2026-05-18T03:50:25.890334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.2428v2","created_at":"2026-05-18T03:50:25.890334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2428","created_at":"2026-05-18T03:50:25.890334+00:00"},{"alias_kind":"pith_short_12","alias_value":"PL3F22TMVIMG","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PL3F22TMVIMGF2PV","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PL3F22TM","created_at":"2026-05-18T12:26:39.201973+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/PL3F22TMVIMGF2PVVAQAUPW4MV","json":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV.json","graph_json":"https://pith.science/api/pith-number/PL3F22TMVIMGF2PVVAQAUPW4MV/graph.json","events_json":"https://pith.science/api/pith-number/PL3F22TMVIMGF2PVVAQAUPW4MV/events.json","paper":"https://pith.science/paper/PL3F22TM"},"agent_actions":{"view_html":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV","download_json":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV.json","view_paper":"https://pith.science/paper/PL3F22TM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.2428&json=true","fetch_graph":"https://pith.science/api/pith-number/PL3F22TMVIMGF2PVVAQAUPW4MV/graph.json","fetch_events":"https://pith.science/api/pith-number/PL3F22TMVIMGF2PVVAQAUPW4MV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV/action/storage_attestation","attest_author":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV/action/author_attestation","sign_citation":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV/action/citation_signature","submit_replication":"https://pith.science/pith/PL3F22TMVIMGF2PVVAQAUPW4MV/action/replication_record"}},"created_at":"2026-05-18T03:50:25.890334+00:00","updated_at":"2026-05-18T03:50:25.890334+00:00"}