{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XGZPSCDOF4TNSDFDHUCFFFJ23C","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":"0b4a781afa1be586f7f4ec8df80354f8163a0a830a6343c5212621675c4f6313","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T05:48:25Z","title_canon_sha256":"ce5ec59d393171b1d14699f95c6249940bf1fd7c5c6d8964562aad40c2e5f366"},"schema_version":"1.0","source":{"id":"1405.5966","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5966","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5966v3","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5966","created_at":"2026-05-18T00:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"XGZPSCDOF4TN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XGZPSCDOF4TNSDFD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XGZPSCDO","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:f5410eff9934584fe30d118444769f75e3be486c6f8f394d7261fd68871849a3","target":"graph","created_at":"2026-05-18T00:57:51Z","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":"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}","authors_text":"B. A. Sethuraman, Gr\\'egory Berhuy, Nadya Markin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T05:48:25Z","title":"Bounds of fast decodability of space time block codes, skew-Hermitian matrices, and Azumaya algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5966","kind":"arxiv","version":3},"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:d603a0d40a3525c48486cb9b35237cc33a17f0ceed5077053a409482e3dfd7bf","target":"record","created_at":"2026-05-18T00:57:51Z","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":"0b4a781afa1be586f7f4ec8df80354f8163a0a830a6343c5212621675c4f6313","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-05-23T05:48:25Z","title_canon_sha256":"ce5ec59d393171b1d14699f95c6249940bf1fd7c5c6d8964562aad40c2e5f366"},"schema_version":"1.0","source":{"id":"1405.5966","kind":"arxiv","version":3}},"canonical_sha256":"b9b2f9086e2f26d90ca33d0452953ad892b2957d571621e3e23e817817145087","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9b2f9086e2f26d90ca33d0452953ad892b2957d571621e3e23e817817145087","first_computed_at":"2026-05-18T00:57:51.817849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:51.817849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sFgKqM5JNJoQ/j+l5RcSJwP1+0fYFja8lLHVfoAhR/JNSbDEfmy3M9As6wlCXbWpDXwPuWtANhe9ungkLMPABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:51.818290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5966","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d603a0d40a3525c48486cb9b35237cc33a17f0ceed5077053a409482e3dfd7bf","sha256:f5410eff9934584fe30d118444769f75e3be486c6f8f394d7261fd68871849a3"],"state_sha256":"85f48f6449a79e56eedd9ec2a3282f072d0670a8f289990a6d85a4fc156e5760"}