{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SVW7CIBC7MWRFVWLOHKMGWQ5GR","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":"6ce4902487d5889c74013a1c5f8861e9980f06842af4ac7633b90b22dc61e560","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-08T06:04:10Z","title_canon_sha256":"058290a1ef3b52dccfc4eba8bad3d727bea8229313a6cde7576440afa0fb482b"},"schema_version":"1.0","source":{"id":"1008.1387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1387","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1387v1","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1387","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"SVW7CIBC7MWR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SVW7CIBC7MWRFVWL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SVW7CIBC","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:64b9dbbc1e05186536c66519c38ac525cb803edb463d6d657efa351f7c7657d3","target":"graph","created_at":"2026-05-18T04:42:24Z","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":"It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding. More precisely, we take the quotient of the algebra by a two-sided ideal which leads to a finite alphabet for the outer code, with a cyclic algebra structure over a finit","authors_text":"Frederique Oggier, Jean-Claude Belfiore, Patrick Sole","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-08T06:04:10Z","title":"Codes over Matrix Rings for Space-Time Coded Modulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1387","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":"sha256:4cf16521d012fefa14fc2f2ee861022e533644dfdcdbcc25d3532aae40c39156","target":"record","created_at":"2026-05-18T04:42:24Z","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":"6ce4902487d5889c74013a1c5f8861e9980f06842af4ac7633b90b22dc61e560","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-08-08T06:04:10Z","title_canon_sha256":"058290a1ef3b52dccfc4eba8bad3d727bea8229313a6cde7576440afa0fb482b"},"schema_version":"1.0","source":{"id":"1008.1387","kind":"arxiv","version":1}},"canonical_sha256":"956df12022fb2d12d6cb71d4c35a1d347a8dc69011285c9df7dcfa930dc498be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"956df12022fb2d12d6cb71d4c35a1d347a8dc69011285c9df7dcfa930dc498be","first_computed_at":"2026-05-18T04:42:24.358027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:24.358027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLVD3+XtXnZj3XKrdveEoC4tnx9iDdDl3YFy0BXSoK3dlwTGFotCxL6HR/s2X/wMCfjBjko9vXg6aCegrzbwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:24.358439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cf16521d012fefa14fc2f2ee861022e533644dfdcdbcc25d3532aae40c39156","sha256:64b9dbbc1e05186536c66519c38ac525cb803edb463d6d657efa351f7c7657d3"],"state_sha256":"b81eac49c6f5ce03ad7aa08e9fa90d2928d8cd3f3903fcfd2de259ef76d18ee0"}