{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IEBFN4MDV2C7NJWAFUMO4R7773","short_pith_number":"pith:IEBFN4MD","canonical_record":{"source":{"id":"1502.01414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-05T02:51:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"530865199ecc4b7655981e80107ae35b0d60d948ece229c2d65d34f1a2698ce6","abstract_canon_sha256":"c8801f1adbff10788189629ce1b72a1aa1aa2c4127f6a88483edf4c6d72a2b81"},"schema_version":"1.0"},"canonical_sha256":"410256f183ae85f6a6c02d18ee47fffee2b4e49afdb6131edaf9b39857fded51","source":{"kind":"arxiv","id":"1502.01414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01414","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01414v1","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01414","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IEBFN4MDV2C7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IEBFN4MDV2C7NJWA","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IEBFN4MD","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IEBFN4MDV2C7NJWAFUMO4R7773","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-05T02:51:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"530865199ecc4b7655981e80107ae35b0d60d948ece229c2d65d34f1a2698ce6","abstract_canon_sha256":"c8801f1adbff10788189629ce1b72a1aa1aa2c4127f6a88483edf4c6d72a2b81"},"schema_version":"1.0"},"canonical_sha256":"410256f183ae85f6a6c02d18ee47fffee2b4e49afdb6131edaf9b39857fded51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:56.615138Z","signature_b64":"kjf2NqkEBEXHQxKhJ5MGq7dg9QvXV1KvmDq3yzJk6jdGvHvwVbtC4G459LP5hV88Pd+Tq6XPhWAAh8H4RP2FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"410256f183ae85f6a6c02d18ee47fffee2b4e49afdb6131edaf9b39857fded51","last_reissued_at":"2026-05-18T02:27:56.614696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:56.614696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01414","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSod9bEhE3T+BP0eZkAXi0xkJWqFQzdvkeRaVBi8A/iu0VHra0OM7OaqjuZwEeeF2QG/oHMkgTwEiyxsw+R8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:11:24.997502Z"},"content_sha256":"c040f766a79061f8c23c22c9076e11a4598b154a0ac92033b74ba4b1cd97d7e5","schema_version":"1.0","event_id":"sha256:c040f766a79061f8c23c22c9076e11a4598b154a0ac92033b74ba4b1cd97d7e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IEBFN4MDV2C7NJWAFUMO4R7773","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic LRC Codes and their Subfield Subcodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Barg, Itzhak Tamo, Robert Calderbank, Sreechakra Goparaju","submitted_at":"2015-02-05T02:51:33Z","abstract_excerpt":"We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Transactions on Information Theory, no. 8, 2014; arXiv:1311.3284). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also stu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01414","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8GK7kbmIMuSLpgSWPSBf93ETAEJPCLra64C3vVGCTk0sk8fCP3/7ZLJPXfAE8jOxz6bccFuNZ1KC6feUI+qFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:11:24.998080Z"},"content_sha256":"b5a65eee74c87be967b1bdd61cf2068b0b221ec43abdfdd89e3197dc0b15c376","schema_version":"1.0","event_id":"sha256:b5a65eee74c87be967b1bdd61cf2068b0b221ec43abdfdd89e3197dc0b15c376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEBFN4MDV2C7NJWAFUMO4R7773/bundle.json","state_url":"https://pith.science/pith/IEBFN4MDV2C7NJWAFUMO4R7773/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEBFN4MDV2C7NJWAFUMO4R7773/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":"2026-06-07T07:11:24Z","links":{"resolver":"https://pith.science/pith/IEBFN4MDV2C7NJWAFUMO4R7773","bundle":"https://pith.science/pith/IEBFN4MDV2C7NJWAFUMO4R7773/bundle.json","state":"https://pith.science/pith/IEBFN4MDV2C7NJWAFUMO4R7773/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEBFN4MDV2C7NJWAFUMO4R7773/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IEBFN4MDV2C7NJWAFUMO4R7773","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":"c8801f1adbff10788189629ce1b72a1aa1aa2c4127f6a88483edf4c6d72a2b81","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-05T02:51:33Z","title_canon_sha256":"530865199ecc4b7655981e80107ae35b0d60d948ece229c2d65d34f1a2698ce6"},"schema_version":"1.0","source":{"id":"1502.01414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01414","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01414v1","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01414","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IEBFN4MDV2C7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IEBFN4MDV2C7NJWA","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IEBFN4MD","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:b5a65eee74c87be967b1bdd61cf2068b0b221ec43abdfdd89e3197dc0b15c376","target":"graph","created_at":"2026-05-18T02:27:56Z","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":"We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg (IEEE Transactions on Information Theory, no. 8, 2014; arXiv:1311.3284). In this paper we focus on the optimal cyclic codes that arise from the general construction. We give a characterization of these codes in terms of their zeros, and observe that there are many equivalent ways of constructing optimal cyclic LRC codes over a given field. We also stu","authors_text":"Alexander Barg, Itzhak Tamo, Robert Calderbank, Sreechakra Goparaju","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-05T02:51:33Z","title":"Cyclic LRC Codes and their Subfield Subcodes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01414","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:c040f766a79061f8c23c22c9076e11a4598b154a0ac92033b74ba4b1cd97d7e5","target":"record","created_at":"2026-05-18T02:27:56Z","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":"c8801f1adbff10788189629ce1b72a1aa1aa2c4127f6a88483edf4c6d72a2b81","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-05T02:51:33Z","title_canon_sha256":"530865199ecc4b7655981e80107ae35b0d60d948ece229c2d65d34f1a2698ce6"},"schema_version":"1.0","source":{"id":"1502.01414","kind":"arxiv","version":1}},"canonical_sha256":"410256f183ae85f6a6c02d18ee47fffee2b4e49afdb6131edaf9b39857fded51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410256f183ae85f6a6c02d18ee47fffee2b4e49afdb6131edaf9b39857fded51","first_computed_at":"2026-05-18T02:27:56.614696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:56.614696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kjf2NqkEBEXHQxKhJ5MGq7dg9QvXV1KvmDq3yzJk6jdGvHvwVbtC4G459LP5hV88Pd+Tq6XPhWAAh8H4RP2FAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:56.615138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c040f766a79061f8c23c22c9076e11a4598b154a0ac92033b74ba4b1cd97d7e5","sha256:b5a65eee74c87be967b1bdd61cf2068b0b221ec43abdfdd89e3197dc0b15c376"],"state_sha256":"32deee27e229eddc43925362dda2fa6a42d559d10dca71a37a58291a01cb3871"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCtmJ82p/2YDHcTBwqdfIA0RE+/VpSM3bZBpev+BeD7QalCzlmiXaaNsnASAegzoNvtKgVE27fetA+3SH3e0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:11:25.001177Z","bundle_sha256":"7b789ba7c3820072adb32ed4e03034cdb731cb7bceec3e9f13dcff9560abbf12"}}