{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AQDMIY7YOINW7IKT3GBMI4UCOR","short_pith_number":"pith:AQDMIY7Y","canonical_record":{"source":{"id":"1204.6564","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-30T07:20:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8c857c8cf29e8966b87b608e27b42ddeea0d6e98012cdb6bac8007bd3156f107","abstract_canon_sha256":"745c36ac055b9099903d49e8b1fbf63a32b58c4ee4f6d4e2a02dbe2e9876a801"},"schema_version":"1.0"},"canonical_sha256":"0406c463f8721b6fa153d982c47282744fa330ede4608e9b2adbaea8e251eef9","source":{"kind":"arxiv","id":"1204.6564","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6564","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6564v3","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6564","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"AQDMIY7YOINW","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AQDMIY7YOINW7IKT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AQDMIY7Y","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AQDMIY7YOINW7IKT3GBMI4UCOR","target":"record","payload":{"canonical_record":{"source":{"id":"1204.6564","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-30T07:20:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"8c857c8cf29e8966b87b608e27b42ddeea0d6e98012cdb6bac8007bd3156f107","abstract_canon_sha256":"745c36ac055b9099903d49e8b1fbf63a32b58c4ee4f6d4e2a02dbe2e9876a801"},"schema_version":"1.0"},"canonical_sha256":"0406c463f8721b6fa153d982c47282744fa330ede4608e9b2adbaea8e251eef9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:28.986928Z","signature_b64":"bIwDpIYZbFshZDN+dOYXSHZSjpXn8CmU1PH2uKKuGKN8j9gPrg3ikEN5f6ANOX5w1hhoqJxB+zqGQEUBZiVbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0406c463f8721b6fa153d982c47282744fa330ede4608e9b2adbaea8e251eef9","last_reissued_at":"2026-05-18T03:37:28.986332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:28.986332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.6564","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWca4Pjb/xNr4muzYRd9YzzzOLwEx5Bp009opmRKTLj8J6gw5qCDl9Znq0a5cX0NngzmrEEujoYxoR25GF53BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:08:30.323060Z"},"content_sha256":"ed1b3249666f9ed0f6939eec1fbf169cd3e12453bbff24d0af2c84e8fa46bf7b","schema_version":"1.0","event_id":"sha256:ed1b3249666f9ed0f6939eec1fbf169cd3e12453bbff24d0af2c84e8fa46bf7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AQDMIY7YOINW7IKT3GBMI4UCOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Family of Low-Complexity STBCs for Four Transmit Antennas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amr Ismail, Hikmet Sari, Jocelyn Fiorina","submitted_at":"2012-04-30T07:20:21Z","abstract_excerpt":"Space-Time Block Codes (STBCs) suffer from a prohibitively high decoding complexity unless the low-complexity decodability property is taken into consideration in the STBC design. For this purpose, several families of STBCs that involve a reduced decoding complexity have been proposed, notably the multi-group decodable and the fast decodable (FD) codes. Recently, a new family of codes that combines both of these families namely the fast group decodable (FGD) codes was proposed. In this paper, we propose a new construction scheme for rate-1 FGD codes for 2^a transmit antennas. The proposed sche"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6564","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQxYIPasytd9e8UIAvgo63Hr9hPr/t705Qjc1TnbCgK5cpnEZ6ij80RptA5gZkCU/YTY9FNYMXVcSewkijNJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:08:30.323405Z"},"content_sha256":"971cd7f71a2272c55a6249d82d22cafd67b85649148a04b4e7a3ad50f85f6edf","schema_version":"1.0","event_id":"sha256:971cd7f71a2272c55a6249d82d22cafd67b85649148a04b4e7a3ad50f85f6edf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/bundle.json","state_url":"https://pith.science/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T23:08:30Z","links":{"resolver":"https://pith.science/pith/AQDMIY7YOINW7IKT3GBMI4UCOR","bundle":"https://pith.science/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/bundle.json","state":"https://pith.science/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQDMIY7YOINW7IKT3GBMI4UCOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AQDMIY7YOINW7IKT3GBMI4UCOR","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":"745c36ac055b9099903d49e8b1fbf63a32b58c4ee4f6d4e2a02dbe2e9876a801","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-30T07:20:21Z","title_canon_sha256":"8c857c8cf29e8966b87b608e27b42ddeea0d6e98012cdb6bac8007bd3156f107"},"schema_version":"1.0","source":{"id":"1204.6564","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6564","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6564v3","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6564","created_at":"2026-05-18T03:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"AQDMIY7YOINW","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AQDMIY7YOINW7IKT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AQDMIY7Y","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:971cd7f71a2272c55a6249d82d22cafd67b85649148a04b4e7a3ad50f85f6edf","target":"graph","created_at":"2026-05-18T03:37:28Z","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":"Space-Time Block Codes (STBCs) suffer from a prohibitively high decoding complexity unless the low-complexity decodability property is taken into consideration in the STBC design. For this purpose, several families of STBCs that involve a reduced decoding complexity have been proposed, notably the multi-group decodable and the fast decodable (FD) codes. Recently, a new family of codes that combines both of these families namely the fast group decodable (FGD) codes was proposed. In this paper, we propose a new construction scheme for rate-1 FGD codes for 2^a transmit antennas. The proposed sche","authors_text":"Amr Ismail, Hikmet Sari, Jocelyn Fiorina","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-30T07:20:21Z","title":"A New Family of Low-Complexity STBCs for Four Transmit Antennas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6564","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:ed1b3249666f9ed0f6939eec1fbf169cd3e12453bbff24d0af2c84e8fa46bf7b","target":"record","created_at":"2026-05-18T03:37:28Z","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":"745c36ac055b9099903d49e8b1fbf63a32b58c4ee4f6d4e2a02dbe2e9876a801","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-30T07:20:21Z","title_canon_sha256":"8c857c8cf29e8966b87b608e27b42ddeea0d6e98012cdb6bac8007bd3156f107"},"schema_version":"1.0","source":{"id":"1204.6564","kind":"arxiv","version":3}},"canonical_sha256":"0406c463f8721b6fa153d982c47282744fa330ede4608e9b2adbaea8e251eef9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0406c463f8721b6fa153d982c47282744fa330ede4608e9b2adbaea8e251eef9","first_computed_at":"2026-05-18T03:37:28.986332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:28.986332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bIwDpIYZbFshZDN+dOYXSHZSjpXn8CmU1PH2uKKuGKN8j9gPrg3ikEN5f6ANOX5w1hhoqJxB+zqGQEUBZiVbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:28.986928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6564","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed1b3249666f9ed0f6939eec1fbf169cd3e12453bbff24d0af2c84e8fa46bf7b","sha256:971cd7f71a2272c55a6249d82d22cafd67b85649148a04b4e7a3ad50f85f6edf"],"state_sha256":"7037374c04974b434a7dda752163ce2ba1e90818037bb9810f587af61ab1abd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcv0UERHxn/fes5rVsqhQiMfHKPLuKRFaYeck9KGCBpBJRg0aFG4B2TiSBSyDGgHecO91dBgeVPRRFKpI5I6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:08:30.325241Z","bundle_sha256":"c27e13b5b4d0abf73f1d6dab85de8609380dc3a4a9ef4bdd765d6c10a76e005c"}}