{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:S2QKBHDG7YZIML4JKAL6J4FPWP","short_pith_number":"pith:S2QKBHDG","canonical_record":{"source":{"id":"2001.04800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-14T14:24:23Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"e8b28339ddd06a61b4c8e4c8bcd1d13e5bd367bafc2e083210caf321a6f33c9e","abstract_canon_sha256":"72100943ce3fe3951afab46e21fbc3f8dbcfd7a8a63e004116770e3a75605b0e"},"schema_version":"1.0"},"canonical_sha256":"96a0a09c66fe32862f895017e4f0afb3c10cc33cfec769ee0d9e8edefc119395","source":{"kind":"arxiv","id":"2001.04800","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.04800","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2001.04800v2","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.04800","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"S2QKBHDG7YZI","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"S2QKBHDG7YZIML4J","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"S2QKBHDG","created_at":"2026-07-05T01:02:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:S2QKBHDG7YZIML4JKAL6J4FPWP","target":"record","payload":{"canonical_record":{"source":{"id":"2001.04800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-14T14:24:23Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"e8b28339ddd06a61b4c8e4c8bcd1d13e5bd367bafc2e083210caf321a6f33c9e","abstract_canon_sha256":"72100943ce3fe3951afab46e21fbc3f8dbcfd7a8a63e004116770e3a75605b0e"},"schema_version":"1.0"},"canonical_sha256":"96a0a09c66fe32862f895017e4f0afb3c10cc33cfec769ee0d9e8edefc119395","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:02:58.093808Z","signature_b64":"0crR0jDdUDArwqr4xMQMPVxdGCzZR2O5KSxpLvSvoa2t7MsonfHxVGspV6ma229D56P4otDqaVJQOnN8oATgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a0a09c66fe32862f895017e4f0afb3c10cc33cfec769ee0d9e8edefc119395","last_reissued_at":"2026-07-05T01:02:58.093441Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:02:58.093441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.04800","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":"2026-07-05T01:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OtmF2AJ4VCgnOKYfsAphcVsYAaVDTwg3fieMlc1Ns0Qn6ApvtttZWtOGKDASOTjX+JZf1LSlOhKd7K+kJmVhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T01:59:33.403848Z"},"content_sha256":"5e5b57721d949da6055f1fa8536cdc68ea387755b28767dfb25ce98618bb44f0","schema_version":"1.0","event_id":"sha256:5e5b57721d949da6055f1fa8536cdc68ea387755b28767dfb25ce98618bb44f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:S2QKBHDG7YZIML4JKAL6J4FPWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Antonia Wachter-Zeh, Camilla Hollanti, Julian Renner, Ragnar Freij-Hollanti, Sven Puchinger","submitted_at":"2020-01-14T14:24:23Z","abstract_excerpt":"We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\\mathbb{Z}_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al.(2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.04800","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.04800/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kr4+EhS/3Q4+iRoylNArYJjg93R1Uus4vDzr43oBHmk8QcSkHC9Zl0u347ohgo9QAof+v59clg+0+YgxgaQiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T01:59:33.404509Z"},"content_sha256":"7cfc307f4d69636633d04245ea9cf6701cee4d28c26358daf178b6049cc4cb7e","schema_version":"1.0","event_id":"sha256:7cfc307f4d69636633d04245ea9cf6701cee4d28c26358daf178b6049cc4cb7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/bundle.json","state_url":"https://pith.science/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/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":"2026-07-07T01:59:33Z","links":{"resolver":"https://pith.science/pith/S2QKBHDG7YZIML4JKAL6J4FPWP","bundle":"https://pith.science/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/bundle.json","state":"https://pith.science/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2QKBHDG7YZIML4JKAL6J4FPWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:S2QKBHDG7YZIML4JKAL6J4FPWP","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":"72100943ce3fe3951afab46e21fbc3f8dbcfd7a8a63e004116770e3a75605b0e","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-14T14:24:23Z","title_canon_sha256":"e8b28339ddd06a61b4c8e4c8bcd1d13e5bd367bafc2e083210caf321a6f33c9e"},"schema_version":"1.0","source":{"id":"2001.04800","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.04800","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2001.04800v2","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.04800","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"S2QKBHDG7YZI","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"S2QKBHDG7YZIML4J","created_at":"2026-07-05T01:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"S2QKBHDG","created_at":"2026-07-05T01:02:58Z"}],"graph_snapshots":[{"event_id":"sha256:7cfc307f4d69636633d04245ea9cf6701cee4d28c26358daf178b6049cc4cb7e","target":"graph","created_at":"2026-07-05T01:02:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.04800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\\mathbb{Z}_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al.(2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upp","authors_text":"Antonia Wachter-Zeh, Camilla Hollanti, Julian Renner, Ragnar Freij-Hollanti, Sven Puchinger","cross_cats":["cs.CR","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-14T14:24:23Z","title":"Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.04800","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":"sha256:5e5b57721d949da6055f1fa8536cdc68ea387755b28767dfb25ce98618bb44f0","target":"record","created_at":"2026-07-05T01:02:58Z","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":"72100943ce3fe3951afab46e21fbc3f8dbcfd7a8a63e004116770e3a75605b0e","cross_cats_sorted":["cs.CR","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-01-14T14:24:23Z","title_canon_sha256":"e8b28339ddd06a61b4c8e4c8bcd1d13e5bd367bafc2e083210caf321a6f33c9e"},"schema_version":"1.0","source":{"id":"2001.04800","kind":"arxiv","version":2}},"canonical_sha256":"96a0a09c66fe32862f895017e4f0afb3c10cc33cfec769ee0d9e8edefc119395","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96a0a09c66fe32862f895017e4f0afb3c10cc33cfec769ee0d9e8edefc119395","first_computed_at":"2026-07-05T01:02:58.093441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:02:58.093441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0crR0jDdUDArwqr4xMQMPVxdGCzZR2O5KSxpLvSvoa2t7MsonfHxVGspV6ma229D56P4otDqaVJQOnN8oATgBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:02:58.093808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.04800","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e5b57721d949da6055f1fa8536cdc68ea387755b28767dfb25ce98618bb44f0","sha256:7cfc307f4d69636633d04245ea9cf6701cee4d28c26358daf178b6049cc4cb7e"],"state_sha256":"36ac82f98ad5c2831ce8f35318080e1b1c50525cb36aaf4c45b38ecf637286b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/9avUAyyMVQ45UU4MvrMG/R65nd8du941A7alHtF8ajw50x9o9eMmU+2uEp1XEMbw4DPMIpOZy8Wy1S9NXMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T01:59:33.408394Z","bundle_sha256":"9a0707a0aa680baddc8d2ded1c70bdaf3b40e57f2060789f0a3428af85c83588"}}