{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XGZPSCDOF4TNSDFDHUCFFFJ23C","short_pith_number":"pith:XGZPSCDO","schema_version":"1.0","canonical_sha256":"b9b2f9086e2f26d90ca33d0452953ad892b2957d571621e3e23e817817145087","source":{"kind":"arxiv","id":"1405.5966","version":3},"attestation_state":"computed","paper":{"title":"Bounds of fast decodability of space time block codes, skew-Hermitian matrices, and Azumaya algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. A. Sethuraman, Gr\\'egory Berhuy, Nadya Markin","submitted_at":"2014-05-23T05:48:25Z","abstract_excerpt":"We study fast lattice decodability of space-time block codes for $n$ transmit and receive antennas, written very generally as a linear combination $\\sum_{i=1}^{2l} s_i A_i$, where the $s_i$ are real information symbols and the $A_i$ are $n\\times n$ $\\mathbb R$-linearly independent complex valued matrices. We show that the mutual orthogonality condition $A_iA_j^* + A_jA_i^*=0$ for distinct basis matrices is not only sufficient but also necessary for fast decodability. We build on this to show that for full-rate ($l = n^2$) transmission, the decoding complexity can be no better than $|S|^{n^2+1}"},"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":"1405.5966","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T05:48:25Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ce5ec59d393171b1d14699f95c6249940bf1fd7c5c6d8964562aad40c2e5f366","abstract_canon_sha256":"0b4a781afa1be586f7f4ec8df80354f8163a0a830a6343c5212621675c4f6313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:51.818290Z","signature_b64":"sFgKqM5JNJoQ/j+l5RcSJwP1+0fYFja8lLHVfoAhR/JNSbDEfmy3M9As6wlCXbWpDXwPuWtANhe9ungkLMPABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9b2f9086e2f26d90ca33d0452953ad892b2957d571621e3e23e817817145087","last_reissued_at":"2026-05-18T00:57:51.817849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:51.817849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds of fast decodability of space time block codes, skew-Hermitian matrices, and Azumaya algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. A. Sethuraman, Gr\\'egory Berhuy, Nadya Markin","submitted_at":"2014-05-23T05:48:25Z","abstract_excerpt":"We study fast lattice decodability of space-time block codes for $n$ transmit and receive antennas, written very generally as a linear combination $\\sum_{i=1}^{2l} s_i A_i$, where the $s_i$ are real information symbols and the $A_i$ are $n\\times n$ $\\mathbb R$-linearly independent complex valued matrices. We show that the mutual orthogonality condition $A_iA_j^* + A_jA_i^*=0$ for distinct basis matrices is not only sufficient but also necessary for fast decodability. We build on this to show that for full-rate ($l = n^2$) transmission, the decoding complexity can be no better than $|S|^{n^2+1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5966","kind":"arxiv","version":3},"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":"1405.5966","created_at":"2026-05-18T00:57:51.817917+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5966v3","created_at":"2026-05-18T00:57:51.817917+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5966","created_at":"2026-05-18T00:57:51.817917+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGZPSCDOF4TN","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGZPSCDOF4TNSDFD","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGZPSCDO","created_at":"2026-05-18T12:28:57.508820+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/XGZPSCDOF4TNSDFDHUCFFFJ23C","json":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C.json","graph_json":"https://pith.science/api/pith-number/XGZPSCDOF4TNSDFDHUCFFFJ23C/graph.json","events_json":"https://pith.science/api/pith-number/XGZPSCDOF4TNSDFDHUCFFFJ23C/events.json","paper":"https://pith.science/paper/XGZPSCDO"},"agent_actions":{"view_html":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C","download_json":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C.json","view_paper":"https://pith.science/paper/XGZPSCDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5966&json=true","fetch_graph":"https://pith.science/api/pith-number/XGZPSCDOF4TNSDFDHUCFFFJ23C/graph.json","fetch_events":"https://pith.science/api/pith-number/XGZPSCDOF4TNSDFDHUCFFFJ23C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C/action/storage_attestation","attest_author":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C/action/author_attestation","sign_citation":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C/action/citation_signature","submit_replication":"https://pith.science/pith/XGZPSCDOF4TNSDFDHUCFFFJ23C/action/replication_record"}},"created_at":"2026-05-18T00:57:51.817917+00:00","updated_at":"2026-05-18T00:57:51.817917+00:00"}