{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PA24INLNZ4QJTUNO6S4THU4DYQ","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":"8fab2078da768bc350b9c843e531579d79a023f5fc5f9ba6ab430394149ec6a3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-06T09:39:03Z","title_canon_sha256":"0ef41331aa3c875595b21469c84fa425bc1e7625c3dcbbade46378526f440094"},"schema_version":"1.0","source":{"id":"1711.01803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01803","created_at":"2026-05-18T00:31:16Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01803v1","created_at":"2026-05-18T00:31:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01803","created_at":"2026-05-18T00:31:16Z"},{"alias_kind":"pith_short_12","alias_value":"PA24INLNZ4QJ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PA24INLNZ4QJTUNO","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PA24INLN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:756a3296383ac8db4867a4b749eecc24ab64cc7ae9a34e0d50762abc877c9e9e","target":"graph","created_at":"2026-05-18T00:31:16Z","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":"This paper gives lower and upper bounds on the covering radius of codes over $\\mathbb{Z}_{p^2}$ with respect to Lee distance. We also determine the covering radius of various Repetition codes over $\\mathbb{Z}_{p^2}.$","authors_text":"C. Durairajan, N. Annamalai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-06T09:39:03Z","title":"On Codes over $\\mathbb{Z}_{p^2}$ and its Covering Radius"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01803","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":"sha256:6d94eb8a1c8009a7f941aa3c463536a32c67e42c2c016c0c9f7eda06f61747ad","target":"record","created_at":"2026-05-18T00:31:16Z","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":"8fab2078da768bc350b9c843e531579d79a023f5fc5f9ba6ab430394149ec6a3","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-06T09:39:03Z","title_canon_sha256":"0ef41331aa3c875595b21469c84fa425bc1e7625c3dcbbade46378526f440094"},"schema_version":"1.0","source":{"id":"1711.01803","kind":"arxiv","version":1}},"canonical_sha256":"7835c4356dcf2099d1aef4b933d383c431ac9c1a86d198085250bb8443a55f42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7835c4356dcf2099d1aef4b933d383c431ac9c1a86d198085250bb8443a55f42","first_computed_at":"2026-05-18T00:31:16.813374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:16.813374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xA/F6fX1K08xYWrGxwt04bx9lOJehbhTUZcPdFkP+viT0ndVrkXFvIBiz0nV2BuHXh67Jaoq/0h+LXmCJlTACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:16.813846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d94eb8a1c8009a7f941aa3c463536a32c67e42c2c016c0c9f7eda06f61747ad","sha256:756a3296383ac8db4867a4b749eecc24ab64cc7ae9a34e0d50762abc877c9e9e"],"state_sha256":"17a635eec4b47aba54594813b73db412f69e3ccb5720bf8cb054c150928f92bd"}