{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O7CNHTP7PZXMKWAKTVQFZTTATH","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":"9ae2e5aff28123d0d8579c16836d7ed31999d8d11fe56398ab231b65a1730f46","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-23T12:16:12Z","title_canon_sha256":"a9bee098db1b65068fd644277837a20b7295210ed2dc22e7e76a2c3e814cde61"},"schema_version":"1.0","source":{"id":"1410.6339","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6339","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6339v2","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6339","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"O7CNHTP7PZXM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O7CNHTP7PZXMKWAK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O7CNHTP7","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:65373018d848052337f9eeb6d7b0989cb51624d23a7b4e77dafd3ea73dd0514b","target":"graph","created_at":"2026-05-18T01:05:12Z","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":"In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repairable code with a good minimum distance. The proof of this also gives a constructive method to find locally repairable codes. Constructions are given of three infinite classes of optimal vector-linear locally repairable codes over an alphabet of small size, not depending on the size of the code.","authors_text":"Camilla Hollanti, Ragnar Freij, Thomas Westerb\\\"ack, Toni Ernvall","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-23T12:16:12Z","title":"Constructions and Properties of Linear Locally Repairable Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6339","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":"sha256:83e5064d3253edb652aa377a2677d2884db798b94b5a1326821cf4c456f3560a","target":"record","created_at":"2026-05-18T01:05:12Z","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":"9ae2e5aff28123d0d8579c16836d7ed31999d8d11fe56398ab231b65a1730f46","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-23T12:16:12Z","title_canon_sha256":"a9bee098db1b65068fd644277837a20b7295210ed2dc22e7e76a2c3e814cde61"},"schema_version":"1.0","source":{"id":"1410.6339","kind":"arxiv","version":2}},"canonical_sha256":"77c4d3cdff7e6ec5580a9d605cce6099ea1ede1e5a576305327127a21ffa3127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77c4d3cdff7e6ec5580a9d605cce6099ea1ede1e5a576305327127a21ffa3127","first_computed_at":"2026-05-18T01:05:12.922355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:12.922355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNkQen2bQdx+TwzB+4EaeM5tfItBxP4p0XXeNqyfdfYgylSwDSBfGVnfU0lJKG1LyEShIB/VOdEkcTcV+MAvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:12.923311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6339","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83e5064d3253edb652aa377a2677d2884db798b94b5a1326821cf4c456f3560a","sha256:65373018d848052337f9eeb6d7b0989cb51624d23a7b4e77dafd3ea73dd0514b"],"state_sha256":"40d1d8be106271e3c96f71a5c8847b3eeb763954d74470838acbae8a537164cb"}