{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SQYVGB2XGNITROOWLAAEDB5DE3","short_pith_number":"pith:SQYVGB2X","canonical_record":{"source":{"id":"1709.02465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-07T22:04:08Z","cross_cats_sorted":[],"title_canon_sha256":"e0957de0ba5f79b7c17d2c769a9dd2adbe22e467438868df0ec73ff320e13cd8","abstract_canon_sha256":"a1e2e91b672d85ce8e72e5585cb0c7bd3302507122bd5e8bb692b455ec003b9e"},"schema_version":"1.0"},"canonical_sha256":"9431530757335138b9d658004187a326ee63ba1313c1dd7ca2978a31d2517efd","source":{"kind":"arxiv","id":"1709.02465","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02465","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02465v2","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02465","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"SQYVGB2XGNIT","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SQYVGB2XGNITROOW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SQYVGB2X","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SQYVGB2XGNITROOWLAAEDB5DE3","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02465","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-07T22:04:08Z","cross_cats_sorted":[],"title_canon_sha256":"e0957de0ba5f79b7c17d2c769a9dd2adbe22e467438868df0ec73ff320e13cd8","abstract_canon_sha256":"a1e2e91b672d85ce8e72e5585cb0c7bd3302507122bd5e8bb692b455ec003b9e"},"schema_version":"1.0"},"canonical_sha256":"9431530757335138b9d658004187a326ee63ba1313c1dd7ca2978a31d2517efd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:38.881595Z","signature_b64":"LK4GJLmBoZp7cMCvfvm18rLVKoV7nOaTif921YCnMQa9WxAa+oC5MPRjnYRmodxaE+RVR3ExZryhLDvnrNbCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9431530757335138b9d658004187a326ee63ba1313c1dd7ca2978a31d2517efd","last_reissued_at":"2026-05-18T00:33:38.880955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:38.880955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02465","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S0JnkDo/Bu16fgiOAT2iK6hV2KslZVWSD5qjr2lWC3vA3hELHnXXC8xMF/SYuM0Lqotcy+84z9ewftexg43aCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:43:03.792419Z"},"content_sha256":"30295e056616bcfe7fbebf11a91489c37904be1858f208d3616e8528b44faea3","schema_version":"1.0","event_id":"sha256:30295e056616bcfe7fbebf11a91489c37904be1858f208d3616e8528b44faea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SQYVGB2XGNITROOWLAAEDB5DE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hadamard Full Propelinear Codes of type Q. Rank and Kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Su\\'arez Canedo, J. Rif\\`a","submitted_at":"2017-09-07T22:04:08Z","abstract_excerpt":"Hadamard full propelinear codes (HFP-codes) are introduced and their equivalence with Hadamard groups is proven (on the other hand, it is already known the equivalence of Hadamard groups with relative $(4n,2,4n,2n)$-difference sets in a group and also with cocyclic Hadamard matrices). We compute the available values for the rank and dimension of the kernel of HFP-codes of type Q and we show that the dimension of the kernel is always 1 or $2$. We also show that when the dimension of the kernel is 2 then the dimension of the kernel of the transposed code is 1 (so, both codes are not equivalent)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02465","kind":"arxiv","version":2},"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":"2026-05-18T00:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HKiablYPJyws2Ysn58i/JRh7pjxWpEQ9yJ/UJS3FnU32GnoadlXujiQi9ZZvP75lRtjA3xPWYAgK55fBwlXMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:43:03.792765Z"},"content_sha256":"fb4418a3316ba1d85cb55d10c6d360db2525dcb2ff434480f2a86e13ee67b247","schema_version":"1.0","event_id":"sha256:fb4418a3316ba1d85cb55d10c6d360db2525dcb2ff434480f2a86e13ee67b247"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQYVGB2XGNITROOWLAAEDB5DE3/bundle.json","state_url":"https://pith.science/pith/SQYVGB2XGNITROOWLAAEDB5DE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQYVGB2XGNITROOWLAAEDB5DE3/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":"2026-06-09T09:43:03Z","links":{"resolver":"https://pith.science/pith/SQYVGB2XGNITROOWLAAEDB5DE3","bundle":"https://pith.science/pith/SQYVGB2XGNITROOWLAAEDB5DE3/bundle.json","state":"https://pith.science/pith/SQYVGB2XGNITROOWLAAEDB5DE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQYVGB2XGNITROOWLAAEDB5DE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SQYVGB2XGNITROOWLAAEDB5DE3","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":"a1e2e91b672d85ce8e72e5585cb0c7bd3302507122bd5e8bb692b455ec003b9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-07T22:04:08Z","title_canon_sha256":"e0957de0ba5f79b7c17d2c769a9dd2adbe22e467438868df0ec73ff320e13cd8"},"schema_version":"1.0","source":{"id":"1709.02465","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02465","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02465v2","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02465","created_at":"2026-05-18T00:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"SQYVGB2XGNIT","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SQYVGB2XGNITROOW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SQYVGB2X","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:fb4418a3316ba1d85cb55d10c6d360db2525dcb2ff434480f2a86e13ee67b247","target":"graph","created_at":"2026-05-18T00:33:38Z","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":"Hadamard full propelinear codes (HFP-codes) are introduced and their equivalence with Hadamard groups is proven (on the other hand, it is already known the equivalence of Hadamard groups with relative $(4n,2,4n,2n)$-difference sets in a group and also with cocyclic Hadamard matrices). We compute the available values for the rank and dimension of the kernel of HFP-codes of type Q and we show that the dimension of the kernel is always 1 or $2$. We also show that when the dimension of the kernel is 2 then the dimension of the kernel of the transposed code is 1 (so, both codes are not equivalent).","authors_text":"E. Su\\'arez Canedo, J. Rif\\`a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-07T22:04:08Z","title":"Hadamard Full Propelinear Codes of type Q. Rank and Kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02465","kind":"arxiv","version":2},"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":"sha256:30295e056616bcfe7fbebf11a91489c37904be1858f208d3616e8528b44faea3","target":"record","created_at":"2026-05-18T00:33:38Z","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":"a1e2e91b672d85ce8e72e5585cb0c7bd3302507122bd5e8bb692b455ec003b9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-07T22:04:08Z","title_canon_sha256":"e0957de0ba5f79b7c17d2c769a9dd2adbe22e467438868df0ec73ff320e13cd8"},"schema_version":"1.0","source":{"id":"1709.02465","kind":"arxiv","version":2}},"canonical_sha256":"9431530757335138b9d658004187a326ee63ba1313c1dd7ca2978a31d2517efd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9431530757335138b9d658004187a326ee63ba1313c1dd7ca2978a31d2517efd","first_computed_at":"2026-05-18T00:33:38.880955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:38.880955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LK4GJLmBoZp7cMCvfvm18rLVKoV7nOaTif921YCnMQa9WxAa+oC5MPRjnYRmodxaE+RVR3ExZryhLDvnrNbCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:38.881595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02465","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30295e056616bcfe7fbebf11a91489c37904be1858f208d3616e8528b44faea3","sha256:fb4418a3316ba1d85cb55d10c6d360db2525dcb2ff434480f2a86e13ee67b247"],"state_sha256":"32be8ae40c855bffa30d5df5e9bcca5acc3b32317a9fb569228546f6c3df08bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QktL3QA2+0c0KWQ4+WmEGOBgbnsCyxGQwEvWJR6RDlU2ZSuQp4psA1ZVPWHQh76LW5RrNRmK1IF7LFph0mO8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:43:03.794720Z","bundle_sha256":"285398f052293db4f6feabf5e3e1e015f311e5bed2c2586cdffb7cda9e80243f"}}