{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BJ4BRGSCSXHC7Q3RLYPIYRXHDH","short_pith_number":"pith:BJ4BRGSC","schema_version":"1.0","canonical_sha256":"0a78189a4295ce2fc3715e1e8c46e719cf91e1a586ddabe13d645074776921fa","source":{"kind":"arxiv","id":"1805.10268","version":4},"attestation_state":"computed","paper":{"title":"Extended Integrated Interleaved Codes over any Field with Applications to Locally Recoverable Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mario Blaum","submitted_at":"2018-05-25T17:40:58Z","abstract_excerpt":"Integrated Interleaved (II) and Extended Integrated Interleaved (EII) codes are a versatile alternative for Locally Recoverable (LRC) codes, since they require fields of relatively small size. II and EII codes are generally defined over Reed-Solomon type of codes. A new comprehensive definition of EII codes is presented, allowing for EII codes over any field, and in particular, over the binary field $GF(2)$. The traditional definition of II and EII codes is shown to be a special case of the new definition. Improvements over previous constructions of LRC codes, in particular, for binary codes, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.10268","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-05-25T17:40:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ce3a827394bec01af5f3fd63f5f0e7db9a15d973446b855943a850af453425bc","abstract_canon_sha256":"5c37b1559224148ff746f7673ed92c2ee5962bbd2047c8c81e1302541d426c17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:03.202730Z","signature_b64":"heY23vNEkci1QlonF/iX/ziygHm8GuY7qhxa+JvFDA+Ask/ha+mPtkW72eX69wCcq2mvGGMrPXMaN3bssd9hDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a78189a4295ce2fc3715e1e8c46e719cf91e1a586ddabe13d645074776921fa","last_reissued_at":"2026-05-17T23:47:03.202048Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:03.202048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extended Integrated Interleaved Codes over any Field with Applications to Locally Recoverable Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mario Blaum","submitted_at":"2018-05-25T17:40:58Z","abstract_excerpt":"Integrated Interleaved (II) and Extended Integrated Interleaved (EII) codes are a versatile alternative for Locally Recoverable (LRC) codes, since they require fields of relatively small size. II and EII codes are generally defined over Reed-Solomon type of codes. A new comprehensive definition of EII codes is presented, allowing for EII codes over any field, and in particular, over the binary field $GF(2)$. The traditional definition of II and EII codes is shown to be a special case of the new definition. Improvements over previous constructions of LRC codes, in particular, for binary codes, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10268","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.10268","created_at":"2026-05-17T23:47:03.202159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10268v4","created_at":"2026-05-17T23:47:03.202159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10268","created_at":"2026-05-17T23:47:03.202159+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJ4BRGSCSXHC","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJ4BRGSCSXHC7Q3R","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJ4BRGSC","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH","json":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH.json","graph_json":"https://pith.science/api/pith-number/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/graph.json","events_json":"https://pith.science/api/pith-number/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/events.json","paper":"https://pith.science/paper/BJ4BRGSC"},"agent_actions":{"view_html":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH","download_json":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH.json","view_paper":"https://pith.science/paper/BJ4BRGSC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10268&json=true","fetch_graph":"https://pith.science/api/pith-number/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/graph.json","fetch_events":"https://pith.science/api/pith-number/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/action/storage_attestation","attest_author":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/action/author_attestation","sign_citation":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/action/citation_signature","submit_replication":"https://pith.science/pith/BJ4BRGSCSXHC7Q3RLYPIYRXHDH/action/replication_record"}},"created_at":"2026-05-17T23:47:03.202159+00:00","updated_at":"2026-05-17T23:47:03.202159+00:00"}