{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WG75KZRUT63TOVOPDLOFXB7CXF","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":"73c998b28d72efe6fcc1ef6bfc856e0dbcdd4cbda40720496dc77af1450bab49","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-06T19:41:27Z","title_canon_sha256":"7c9bc489de7d32b78d96fcc52a717a476ee7f332810a779ed313aad8d92469b6"},"schema_version":"1.0","source":{"id":"1104.1171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1171","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1171v1","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1171","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"WG75KZRUT63T","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WG75KZRUT63TOVOP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WG75KZRU","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:b19c2fa404ce5a1c107065f28991caffa8e0b05d156444231fdf3a57ec5a91aa","target":"graph","created_at":"2026-05-18T04:24:53Z","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":"The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field $\\mathbb{F}_q$ correspond to $\\mathbb{F}_q$-linear quantum codes. Although this connection is straightforward, it does not appear to have been made earlier in literature. The correspondence is made through isotropic subspaces. We also show that the popular Calderbank-Shor-Steane (CSS) codes are essentially the homogenous symplectic matroids while the graph states, which ","authors_text":"Pradeep Sarvepalli","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-06T19:41:27Z","title":"Quantum Codes and Symplectic Matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1171","kind":"arxiv","version":1},"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":"sha256:344dfb9a48ca022aaabb9afe1c93f7bc56e3ba2a6e232d3d5bdd9c9df8af87b9","target":"record","created_at":"2026-05-18T04:24:53Z","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":"73c998b28d72efe6fcc1ef6bfc856e0dbcdd4cbda40720496dc77af1450bab49","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-06T19:41:27Z","title_canon_sha256":"7c9bc489de7d32b78d96fcc52a717a476ee7f332810a779ed313aad8d92469b6"},"schema_version":"1.0","source":{"id":"1104.1171","kind":"arxiv","version":1}},"canonical_sha256":"b1bfd566349fb73755cf1adc5b87e2b96cb497001bf4df4cfe5aeaeab131f431","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1bfd566349fb73755cf1adc5b87e2b96cb497001bf4df4cfe5aeaeab131f431","first_computed_at":"2026-05-18T04:24:53.470202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.470202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SudKwSEbk1A+mBzL+JEFT85WPk6Q+X1tuAX5aIJMHsqpwZWJS9R95KOsyJa8BX7wHca1t6GGjhRJ3K+HmL1OAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.470728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:344dfb9a48ca022aaabb9afe1c93f7bc56e3ba2a6e232d3d5bdd9c9df8af87b9","sha256:b19c2fa404ce5a1c107065f28991caffa8e0b05d156444231fdf3a57ec5a91aa"],"state_sha256":"8b87d080953eeb7ae7c739c6b25cea278b840a1de7edef2677f7ee905e8c7468"}