{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:H7D2AGOJITIPGLH3CJURLJ7WJF","short_pith_number":"pith:H7D2AGOJ","canonical_record":{"source":{"id":"1208.2361","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-08-11T15:38:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c67ceb13c5ef5d861ba591c8b2f5bdfbc0421637baf1f0228116c43dfda07504","abstract_canon_sha256":"58165b1f87763d5178321e69c38dc4984dd330e2a241272edc43e0421d680f0c"},"schema_version":"1.0"},"canonical_sha256":"3fc7a019c944d0f32cfb126915a7f6496c6b34f4c4b829f9e57a1798dd6a6adf","source":{"kind":"arxiv","id":"1208.2361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2361","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2361v2","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2361","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"H7D2AGOJITIP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H7D2AGOJITIPGLH3","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H7D2AGOJ","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:H7D2AGOJITIPGLH3CJURLJ7WJF","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2361","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-08-11T15:38:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c67ceb13c5ef5d861ba591c8b2f5bdfbc0421637baf1f0228116c43dfda07504","abstract_canon_sha256":"58165b1f87763d5178321e69c38dc4984dd330e2a241272edc43e0421d680f0c"},"schema_version":"1.0"},"canonical_sha256":"3fc7a019c944d0f32cfb126915a7f6496c6b34f4c4b829f9e57a1798dd6a6adf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:01.262458Z","signature_b64":"ugHpiEdUldoBcAGfyGyWpmEoWKXLuXtZu9WPfhBNuxnYsCG+3lkPn7r/tlPlXOe+73TIc35GnqJonb0c48T3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fc7a019c944d0f32cfb126915a7f6496c6b34f4c4b829f9e57a1798dd6a6adf","last_reissued_at":"2026-05-18T02:21:01.261934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:01.261934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2361","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOPNqvQ00UyTWecvUvc8jgUoTg3V8N6+2KTa3sMIa3U8ubPgzLziCXp5W8v2EO+r4cMypPeJPAUjY7ZJNC2nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:40:32.063354Z"},"content_sha256":"9d60a6621fceb4bf1fb61cd67982366acba8eb008282d995f497985fde11da7a","schema_version":"1.0","event_id":"sha256:9d60a6621fceb4bf1fb61cd67982366acba8eb008282d995f497985fde11da7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:H7D2AGOJITIPGLH3CJURLJ7WJF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lexicodes over Rings","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kenza Guenda, S. Arash Sheikholeslam, T. Aaron Gulliver","submitted_at":"2012-08-11T15:38:50Z","abstract_excerpt":"In this paper, we consider the construction of linear lexicodes over finite chain rings by using a $B$-ordering over these rings and a selection criterion. % and a greedy Algorithm. As examples we give lexicodes over $\\mathbb{Z}_4$ and $\\mathbb{F}_2+u\\mathbb{F}_2$. %First, greedy algorithms are presented to construct %lexicodes using a multiplicative property. Then, greedy algorithms %are given for the case when the selection criteria is not %multiplicative such as the minimum distance constraint. It is shown that this construction produces many optimal codes over rings and also good binary co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2361","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TTiFXq/zmON5G7TNl9B+5qb3lVjqBEmCD85LwmGClQi6gvPcWgOGre+/+TUsWMYm79xu7dexb+eF3WR2q9A8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:40:32.063721Z"},"content_sha256":"5114af63b53e5bea4341a693aea3d3576c281d1f5bd80dca0d970629f0b12e3e","schema_version":"1.0","event_id":"sha256:5114af63b53e5bea4341a693aea3d3576c281d1f5bd80dca0d970629f0b12e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/bundle.json","state_url":"https://pith.science/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T23:40:32Z","links":{"resolver":"https://pith.science/pith/H7D2AGOJITIPGLH3CJURLJ7WJF","bundle":"https://pith.science/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/bundle.json","state":"https://pith.science/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H7D2AGOJITIPGLH3CJURLJ7WJF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H7D2AGOJITIPGLH3CJURLJ7WJF","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":"58165b1f87763d5178321e69c38dc4984dd330e2a241272edc43e0421d680f0c","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-08-11T15:38:50Z","title_canon_sha256":"c67ceb13c5ef5d861ba591c8b2f5bdfbc0421637baf1f0228116c43dfda07504"},"schema_version":"1.0","source":{"id":"1208.2361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2361","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2361v2","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2361","created_at":"2026-05-18T02:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"H7D2AGOJITIP","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H7D2AGOJITIPGLH3","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H7D2AGOJ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:5114af63b53e5bea4341a693aea3d3576c281d1f5bd80dca0d970629f0b12e3e","target":"graph","created_at":"2026-05-18T02:21:01Z","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, we consider the construction of linear lexicodes over finite chain rings by using a $B$-ordering over these rings and a selection criterion. % and a greedy Algorithm. As examples we give lexicodes over $\\mathbb{Z}_4$ and $\\mathbb{F}_2+u\\mathbb{F}_2$. %First, greedy algorithms are presented to construct %lexicodes using a multiplicative property. Then, greedy algorithms %are given for the case when the selection criteria is not %multiplicative such as the minimum distance constraint. It is shown that this construction produces many optimal codes over rings and also good binary co","authors_text":"Kenza Guenda, S. Arash Sheikholeslam, T. Aaron Gulliver","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-08-11T15:38:50Z","title":"Lexicodes over Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2361","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":"sha256:9d60a6621fceb4bf1fb61cd67982366acba8eb008282d995f497985fde11da7a","target":"record","created_at":"2026-05-18T02:21:01Z","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":"58165b1f87763d5178321e69c38dc4984dd330e2a241272edc43e0421d680f0c","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.IT","submitted_at":"2012-08-11T15:38:50Z","title_canon_sha256":"c67ceb13c5ef5d861ba591c8b2f5bdfbc0421637baf1f0228116c43dfda07504"},"schema_version":"1.0","source":{"id":"1208.2361","kind":"arxiv","version":2}},"canonical_sha256":"3fc7a019c944d0f32cfb126915a7f6496c6b34f4c4b829f9e57a1798dd6a6adf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fc7a019c944d0f32cfb126915a7f6496c6b34f4c4b829f9e57a1798dd6a6adf","first_computed_at":"2026-05-18T02:21:01.261934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:01.261934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ugHpiEdUldoBcAGfyGyWpmEoWKXLuXtZu9WPfhBNuxnYsCG+3lkPn7r/tlPlXOe+73TIc35GnqJonb0c48T3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:01.262458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d60a6621fceb4bf1fb61cd67982366acba8eb008282d995f497985fde11da7a","sha256:5114af63b53e5bea4341a693aea3d3576c281d1f5bd80dca0d970629f0b12e3e"],"state_sha256":"c96242dee4c85779ad8a5b932feb97d73da6a40c1acf40e3de7e87d638ab251e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yG0on2oRrBJsrA0DRudpr+OtZyOaXU/xqAmMQ5bPEL9gdm3OToPlqUnBmSykUQG0tfisKgCkY7LlWOzdqQoGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:40:32.066086Z","bundle_sha256":"d6342f7594ceb740e920b4cc3a81d3fe26bdd4f17923df9065151f524b8b4194"}}