{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XSXJIOKVTFWEMG37PU5G2IWCYE","short_pith_number":"pith:XSXJIOKV","canonical_record":{"source":{"id":"1701.00210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-01T06:01:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"902b5354c66506433e1786534dea15e6aecad0faaaccd8184e7feb63b8980edc","abstract_canon_sha256":"041ecc4024f637840932a7f7c35924b3b82505392af4efb2abe2629d6fcc7b52"},"schema_version":"1.0"},"canonical_sha256":"bcae943955996c461b7f7d3a6d22c2c134e817704ce457280dc07975a03fb187","source":{"kind":"arxiv","id":"1701.00210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00210","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00210v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00210","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"XSXJIOKVTFWE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XSXJIOKVTFWEMG37","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XSXJIOKV","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XSXJIOKVTFWEMG37PU5G2IWCYE","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-01T06:01:29Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"902b5354c66506433e1786534dea15e6aecad0faaaccd8184e7feb63b8980edc","abstract_canon_sha256":"041ecc4024f637840932a7f7c35924b3b82505392af4efb2abe2629d6fcc7b52"},"schema_version":"1.0"},"canonical_sha256":"bcae943955996c461b7f7d3a6d22c2c134e817704ce457280dc07975a03fb187","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:36.075627Z","signature_b64":"fCbMuFthF9Fmyq4ysEnDpyZkHs/GEs5CBJIjFD8oM20Rzeq8iIHSCWvrS9nuZTuTThV08vPQkPuhEYHraZMuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcae943955996c461b7f7d3a6d22c2c134e817704ce457280dc07975a03fb187","last_reissued_at":"2026-05-18T00:53:36.075188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:36.075188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00210","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":"2026-05-18T00:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30/kP7iiaQwW0wsqZLXQgHU33y46iD1TogZgd7gTj9yZ6LGaynBVI7lNTdrnKNtGZDdnHzKg9ftAm08ptuAbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:52:25.613289Z"},"content_sha256":"430523fb055b41762a2ce7eebb64c4abe3274e2674101774b10f27d2036dbc35","schema_version":"1.0","event_id":"sha256:430523fb055b41762a2ce7eebb64c4abe3274e2674101774b10f27d2036dbc35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XSXJIOKVTFWEMG37PU5G2IWCYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction and Encoding of QC-LDPC Codes Using Group Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dariush Kiani, Hassan Khodaiemehr","submitted_at":"2017-01-01T06:01:29Z","abstract_excerpt":"Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from group rings. A group ring is a free module (at the same time a ring) constructed in a natural way from any given ring and any given group. We present a structure based on the elements of a group ring for constructing QC-LDPC codes. Some of the previously addressed methods for constructing QC-LDPC codes based on finite fields are special cases of the proposed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00210","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":"2026-05-18T00:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaG72Djp7vOou0tzGNhuCYDkIR2jb3R7s0P3tOEVRdPj+ED1137s3IjIJfMVV5+3u7xleoMSCAMdD3P664EwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:52:25.613725Z"},"content_sha256":"70122f5ac980c95bd0b3e5af22b0d602e3bda31668a9b9d142b62bbf8d5838af","schema_version":"1.0","event_id":"sha256:70122f5ac980c95bd0b3e5af22b0d602e3bda31668a9b9d142b62bbf8d5838af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/bundle.json","state_url":"https://pith.science/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/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":"2026-05-31T06:52:25Z","links":{"resolver":"https://pith.science/pith/XSXJIOKVTFWEMG37PU5G2IWCYE","bundle":"https://pith.science/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/bundle.json","state":"https://pith.science/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSXJIOKVTFWEMG37PU5G2IWCYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XSXJIOKVTFWEMG37PU5G2IWCYE","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":"041ecc4024f637840932a7f7c35924b3b82505392af4efb2abe2629d6fcc7b52","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-01T06:01:29Z","title_canon_sha256":"902b5354c66506433e1786534dea15e6aecad0faaaccd8184e7feb63b8980edc"},"schema_version":"1.0","source":{"id":"1701.00210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00210","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00210v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00210","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"XSXJIOKVTFWE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XSXJIOKVTFWEMG37","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XSXJIOKV","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:70122f5ac980c95bd0b3e5af22b0d602e3bda31668a9b9d142b62bbf8d5838af","target":"graph","created_at":"2026-05-18T00:53:36Z","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":"Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from group rings. A group ring is a free module (at the same time a ring) constructed in a natural way from any given ring and any given group. We present a structure based on the elements of a group ring for constructing QC-LDPC codes. Some of the previously addressed methods for constructing QC-LDPC codes based on finite fields are special cases of the proposed","authors_text":"Dariush Kiani, Hassan Khodaiemehr","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-01T06:01:29Z","title":"Construction and Encoding of QC-LDPC Codes Using Group Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00210","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":"sha256:430523fb055b41762a2ce7eebb64c4abe3274e2674101774b10f27d2036dbc35","target":"record","created_at":"2026-05-18T00:53:36Z","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":"041ecc4024f637840932a7f7c35924b3b82505392af4efb2abe2629d6fcc7b52","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-01T06:01:29Z","title_canon_sha256":"902b5354c66506433e1786534dea15e6aecad0faaaccd8184e7feb63b8980edc"},"schema_version":"1.0","source":{"id":"1701.00210","kind":"arxiv","version":1}},"canonical_sha256":"bcae943955996c461b7f7d3a6d22c2c134e817704ce457280dc07975a03fb187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcae943955996c461b7f7d3a6d22c2c134e817704ce457280dc07975a03fb187","first_computed_at":"2026-05-18T00:53:36.075188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:36.075188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCbMuFthF9Fmyq4ysEnDpyZkHs/GEs5CBJIjFD8oM20Rzeq8iIHSCWvrS9nuZTuTThV08vPQkPuhEYHraZMuCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:36.075627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:430523fb055b41762a2ce7eebb64c4abe3274e2674101774b10f27d2036dbc35","sha256:70122f5ac980c95bd0b3e5af22b0d602e3bda31668a9b9d142b62bbf8d5838af"],"state_sha256":"f125f8ecb617d2edf6277b55b70e8a044ecba7545a6459180281755d906c9b09"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vd6ImvHqYuUCEhMQBmBTonWAcqPEhDYi8F057cQc7WKwN3xKqSC9BnZSclnfrA89qNvfTgkYAOjeRD2Ec2JrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:52:25.616283Z","bundle_sha256":"0537f8885c744120567a3cdb617e1d28e0a733669a9c8402fa77dc7653f3b953"}}