{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NNQUXGRAFRYNJNUGWC3VTCWQTH","short_pith_number":"pith:NNQUXGRA","canonical_record":{"source":{"id":"1803.08141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-21T21:08:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d6ecd58d918261486b7a5c869acad60b1dd3711ebd9329ffe4708a5df107883c","abstract_canon_sha256":"700dc2ffc2c88bde533a2de6b5a45d673c7b37e23543fe28cbac1be56585c642"},"schema_version":"1.0"},"canonical_sha256":"6b614b9a202c70d4b686b0b7598ad099c4293eba176eba5a2549574d82056163","source":{"kind":"arxiv","id":"1803.08141","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08141","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08141v1","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08141","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"NNQUXGRAFRYN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NNQUXGRAFRYNJNUG","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NNQUXGRA","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NNQUXGRAFRYNJNUGWC3VTCWQTH","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-21T21:08:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d6ecd58d918261486b7a5c869acad60b1dd3711ebd9329ffe4708a5df107883c","abstract_canon_sha256":"700dc2ffc2c88bde533a2de6b5a45d673c7b37e23543fe28cbac1be56585c642"},"schema_version":"1.0"},"canonical_sha256":"6b614b9a202c70d4b686b0b7598ad099c4293eba176eba5a2549574d82056163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:23.578957Z","signature_b64":"RDehajcr03bFgp031i/+JfSoVs9VNAeAJTcwmcko2y+lN4yvdizVIeY1zA46XxL2X3YxTxXpLW9GUfspQCkcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b614b9a202c70d4b686b0b7598ad099c4293eba176eba5a2549574d82056163","last_reissued_at":"2026-05-18T00:20:23.578460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:23.578460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08141","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOltb93nA3kR3/bMZB3xXViKpTihyvAcDstXw0QP998z55CGe/S0KI7LCQQukOSF5aEp6OLO5DwiJQGLSjfYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:55:05.097612Z"},"content_sha256":"e7354ba350e7d93f7126de25ec8b8875262f54920ab405b74df269e2b03a2a2a","schema_version":"1.0","event_id":"sha256:e7354ba350e7d93f7126de25ec8b8875262f54920ab405b74df269e2b03a2a2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NNQUXGRAFRYNJNUGWC3VTCWQTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Search of QC-LDPC Codes with Girths 6 and 8 and Free of Elementary Trapping Sets with Small Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farzane Amirzade, Mohammad-Reza Sadeghi","submitted_at":"2018-03-21T21:08:26Z","abstract_excerpt":"One of the phenomena that influences significantly the performance of low-density parity-check codes is known as trapping sets. An $(a,b)$ elementary trapping set, or simply an ETS where $a$ is the size and $b$ is the number of degree-one check nodes and $\\frac{b}{a}<1$, causes high decoding failure rate and exert a strong influence on the error floor. In this paper, we provide sufficient conditions for exponent matrices to have fully connected $(3,n)$-regular QC-LDPC codes with girths 6 and 8 whose Tanner graphs are free of small ETSs. Applying sufficient conditions on the exponent matrix to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08141","kind":"arxiv","version":1},"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":"2026-05-18T00:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyTO9FvO4gP43grBehFZ91kww+Lp7Id9jBKZLEHowIkOhx7202P8oQJKWCKqXRUsc2BN5akpfupK5v3XWhCmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:55:05.098359Z"},"content_sha256":"05947b41c66570d6f760643e4461ced8d629a51391888424eee40bec19dd1439","schema_version":"1.0","event_id":"sha256:05947b41c66570d6f760643e4461ced8d629a51391888424eee40bec19dd1439"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/bundle.json","state_url":"https://pith.science/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/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":"2026-05-31T08:55:05Z","links":{"resolver":"https://pith.science/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH","bundle":"https://pith.science/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/bundle.json","state":"https://pith.science/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNQUXGRAFRYNJNUGWC3VTCWQTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NNQUXGRAFRYNJNUGWC3VTCWQTH","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":"700dc2ffc2c88bde533a2de6b5a45d673c7b37e23543fe28cbac1be56585c642","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-21T21:08:26Z","title_canon_sha256":"d6ecd58d918261486b7a5c869acad60b1dd3711ebd9329ffe4708a5df107883c"},"schema_version":"1.0","source":{"id":"1803.08141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08141","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08141v1","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08141","created_at":"2026-05-18T00:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"NNQUXGRAFRYN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NNQUXGRAFRYNJNUG","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NNQUXGRA","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:05947b41c66570d6f760643e4461ced8d629a51391888424eee40bec19dd1439","target":"graph","created_at":"2026-05-18T00:20:23Z","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":"One of the phenomena that influences significantly the performance of low-density parity-check codes is known as trapping sets. An $(a,b)$ elementary trapping set, or simply an ETS where $a$ is the size and $b$ is the number of degree-one check nodes and $\\frac{b}{a}<1$, causes high decoding failure rate and exert a strong influence on the error floor. In this paper, we provide sufficient conditions for exponent matrices to have fully connected $(3,n)$-regular QC-LDPC codes with girths 6 and 8 whose Tanner graphs are free of small ETSs. Applying sufficient conditions on the exponent matrix to ","authors_text":"Farzane Amirzade, Mohammad-Reza Sadeghi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-21T21:08:26Z","title":"Efficient Search of QC-LDPC Codes with Girths 6 and 8 and Free of Elementary Trapping Sets with Small Size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08141","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:e7354ba350e7d93f7126de25ec8b8875262f54920ab405b74df269e2b03a2a2a","target":"record","created_at":"2026-05-18T00:20:23Z","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":"700dc2ffc2c88bde533a2de6b5a45d673c7b37e23543fe28cbac1be56585c642","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-03-21T21:08:26Z","title_canon_sha256":"d6ecd58d918261486b7a5c869acad60b1dd3711ebd9329ffe4708a5df107883c"},"schema_version":"1.0","source":{"id":"1803.08141","kind":"arxiv","version":1}},"canonical_sha256":"6b614b9a202c70d4b686b0b7598ad099c4293eba176eba5a2549574d82056163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b614b9a202c70d4b686b0b7598ad099c4293eba176eba5a2549574d82056163","first_computed_at":"2026-05-18T00:20:23.578460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:23.578460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RDehajcr03bFgp031i/+JfSoVs9VNAeAJTcwmcko2y+lN4yvdizVIeY1zA46XxL2X3YxTxXpLW9GUfspQCkcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:23.578957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7354ba350e7d93f7126de25ec8b8875262f54920ab405b74df269e2b03a2a2a","sha256:05947b41c66570d6f760643e4461ced8d629a51391888424eee40bec19dd1439"],"state_sha256":"596ddecffe15dd30fc480d72a572f936ebbcf10a8b80c480d35f1250d324c5a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCcLQ5GsMDUR8tuI40CRq6EgN1x/0jbxZUYXWM98VlyZM6Q6TjhhacjUynLKM2pRHFzACd/y5q8en8uthJuOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:55:05.101824Z","bundle_sha256":"73d998c9d348cd2de5b556cea8042016e51d3d9c9e920ff1b65fce0f2094095d"}}