{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WHQEV6XJIBULLILMNJ7BOBQV6I","short_pith_number":"pith:WHQEV6XJ","schema_version":"1.0","canonical_sha256":"b1e04afae94068b5a16c6a7e170615f20ec91e059000622600352ff30d2e7efd","source":{"kind":"arxiv","id":"1211.4056","version":1},"attestation_state":"computed","paper":{"title":"Two Approaches to the Construction of Deletion Correcting Codes: Weight Partitioning and Optimal Colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ankur A. Kulkarni, Daniel Cullina, Negar Kiyavash","submitted_at":"2012-11-16T22:30:24Z","abstract_excerpt":"We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a code by taking the union of many constant Hamming weight codes. This results in codes that have additional structure. Searching for codes in constant Hamming weight induced subgraphs is computationally easier than searching the original graph. We prove a lower bound on size of a codebook constructed this way for any number of deletions and show that it is only"},"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":"1211.4056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-11-16T22:30:24Z","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"title_canon_sha256":"36c3d294d5d4446651f123ca540d789f0c4b4f3817aa3ef457d0248e182a422e","abstract_canon_sha256":"58935a71631552cd9d2e43ae8e3de860a733c9937543c6f586eb19113b180dd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:28.158066Z","signature_b64":"UophdxLdr1X5KhC9GYyWypQtpluJU+KW/ILCQo3bPrLjIHgi24L0xQG3OfUjC/0EumFwQgINWSlROZy/W+SYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e04afae94068b5a16c6a7e170615f20ec91e059000622600352ff30d2e7efd","last_reissued_at":"2026-05-18T03:40:28.157624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:28.157624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two Approaches to the Construction of Deletion Correcting Codes: Weight Partitioning and Optimal Colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ankur A. Kulkarni, Daniel Cullina, Negar Kiyavash","submitted_at":"2012-11-16T22:30:24Z","abstract_excerpt":"We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a code by taking the union of many constant Hamming weight codes. This results in codes that have additional structure. Searching for codes in constant Hamming weight induced subgraphs is computationally easier than searching the original graph. We prove a lower bound on size of a codebook constructed this way for any number of deletions and show that it is only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4056","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.4056","created_at":"2026-05-18T03:40:28.157682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4056v1","created_at":"2026-05-18T03:40:28.157682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4056","created_at":"2026-05-18T03:40:28.157682+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHQEV6XJIBUL","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHQEV6XJIBULLILM","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHQEV6XJ","created_at":"2026-05-18T12:27:25.539911+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/WHQEV6XJIBULLILMNJ7BOBQV6I","json":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I.json","graph_json":"https://pith.science/api/pith-number/WHQEV6XJIBULLILMNJ7BOBQV6I/graph.json","events_json":"https://pith.science/api/pith-number/WHQEV6XJIBULLILMNJ7BOBQV6I/events.json","paper":"https://pith.science/paper/WHQEV6XJ"},"agent_actions":{"view_html":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I","download_json":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I.json","view_paper":"https://pith.science/paper/WHQEV6XJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4056&json=true","fetch_graph":"https://pith.science/api/pith-number/WHQEV6XJIBULLILMNJ7BOBQV6I/graph.json","fetch_events":"https://pith.science/api/pith-number/WHQEV6XJIBULLILMNJ7BOBQV6I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I/action/storage_attestation","attest_author":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I/action/author_attestation","sign_citation":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I/action/citation_signature","submit_replication":"https://pith.science/pith/WHQEV6XJIBULLILMNJ7BOBQV6I/action/replication_record"}},"created_at":"2026-05-18T03:40:28.157682+00:00","updated_at":"2026-05-18T03:40:28.157682+00:00"}