{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:L463H3YRQHONPNKSMSIVUQ33TS","short_pith_number":"pith:L463H3YR","schema_version":"1.0","canonical_sha256":"5f3db3ef1181dcd7b55264915a437b9ca4d3a2137dc8356fcc9408e4ca407827","source":{"kind":"arxiv","id":"1404.3447","version":1},"attestation_state":"computed","paper":{"title":"Group homomorphisms as error correcting codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.IT"],"primary_cat":"cs.IT","authors_text":"Alan Guo","submitted_at":"2014-04-14T01:45:15Z","abstract_excerpt":"We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup struct"},"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":"1404.3447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-04-14T01:45:15Z","cross_cats_sorted":["math.GR","math.IT"],"title_canon_sha256":"311555a38281e5433c322ebe32c6eb833f9d150b18fb39406d6ead10f5b9eda1","abstract_canon_sha256":"6c92fcadc83b37708d9173ca4139c62608bd6a3c8808f79917fa55264178c4c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:15.169192Z","signature_b64":"pIufyMQaVdk/p40XIwE8F7yda7zP88zLbq8J2i/Ma14Mellcr5oYLSWxej4q14EU9hYopBYxJv7sDeiZRU/yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f3db3ef1181dcd7b55264915a437b9ca4d3a2137dc8356fcc9408e4ca407827","last_reissued_at":"2026-05-18T02:54:15.168760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:15.168760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group homomorphisms as error correcting codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.IT"],"primary_cat":"cs.IT","authors_text":"Alan Guo","submitted_at":"2014-04-14T01:45:15Z","abstract_excerpt":"We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup struct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3447","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":"1404.3447","created_at":"2026-05-18T02:54:15.168834+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.3447v1","created_at":"2026-05-18T02:54:15.168834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3447","created_at":"2026-05-18T02:54:15.168834+00:00"},{"alias_kind":"pith_short_12","alias_value":"L463H3YRQHON","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"L463H3YRQHONPNKS","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"L463H3YR","created_at":"2026-05-18T12:28:35.611951+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/L463H3YRQHONPNKSMSIVUQ33TS","json":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS.json","graph_json":"https://pith.science/api/pith-number/L463H3YRQHONPNKSMSIVUQ33TS/graph.json","events_json":"https://pith.science/api/pith-number/L463H3YRQHONPNKSMSIVUQ33TS/events.json","paper":"https://pith.science/paper/L463H3YR"},"agent_actions":{"view_html":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS","download_json":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS.json","view_paper":"https://pith.science/paper/L463H3YR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.3447&json=true","fetch_graph":"https://pith.science/api/pith-number/L463H3YRQHONPNKSMSIVUQ33TS/graph.json","fetch_events":"https://pith.science/api/pith-number/L463H3YRQHONPNKSMSIVUQ33TS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS/action/storage_attestation","attest_author":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS/action/author_attestation","sign_citation":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS/action/citation_signature","submit_replication":"https://pith.science/pith/L463H3YRQHONPNKSMSIVUQ33TS/action/replication_record"}},"created_at":"2026-05-18T02:54:15.168834+00:00","updated_at":"2026-05-18T02:54:15.168834+00:00"}