{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A4P2TKU4ROJWM7QZ2VPEQBNNSK","short_pith_number":"pith:A4P2TKU4","schema_version":"1.0","canonical_sha256":"071fa9aa9c8b93667e19d55e4805ad92b51136dc4d888bb5aa28a7e6140cc4cb","source":{"kind":"arxiv","id":"2607.02377","version":1},"attestation_state":"computed","paper":{"title":"Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Guangyue Han, Haibin Kan, Yang Xu","submitted_at":"2026-07-02T16:17:16Z","abstract_excerpt":"In this paper, we study generalized rank weights (GRWs) and extended generalized poset weight (EGPWs) of codes over rings via a Galois connection approach. First, we show that various coding-theoretic properties related to generalized weights, including security drops of a code employed in wire-tap channel of type II, connections between generalized weights of a Gabidulin code and its associated Delsarte code, (generalized) Singleton bound, MDS discrepancy of a code, characterizations of MDS, near MDS, $i$-MDS, MRD, near MRD, $i$-MRD, (dually) quasi-MRD codes as well as evasive property of sub"},"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":"2607.02377","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-07-02T16:17:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"dcb05c96164cf69deae32e2659de18506d5ceba545d59179a18f8d66bc840940","abstract_canon_sha256":"dbb720a654b35324b78b1b7c8ec71659282110ddb3d5a2d78f1cb9fbd7debaca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:57.167469Z","signature_b64":"6ucJLw8VuEiBanF64KS3s3JnXiVWLGGIf71cDybbbCh8ovfg4kQKX1ccobrKFFGD2cYfoq6dOncWWeeXOV69Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"071fa9aa9c8b93667e19d55e4805ad92b51136dc4d888bb5aa28a7e6140cc4cb","last_reissued_at":"2026-07-03T01:17:57.167070Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:57.167070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Guangyue Han, Haibin Kan, Yang Xu","submitted_at":"2026-07-02T16:17:16Z","abstract_excerpt":"In this paper, we study generalized rank weights (GRWs) and extended generalized poset weight (EGPWs) of codes over rings via a Galois connection approach. First, we show that various coding-theoretic properties related to generalized weights, including security drops of a code employed in wire-tap channel of type II, connections between generalized weights of a Gabidulin code and its associated Delsarte code, (generalized) Singleton bound, MDS discrepancy of a code, characterizations of MDS, near MDS, $i$-MDS, MRD, near MRD, $i$-MRD, (dually) quasi-MRD codes as well as evasive property of sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02377","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02377/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.02377","created_at":"2026-07-03T01:17:57.167127+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.02377v1","created_at":"2026-07-03T01:17:57.167127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02377","created_at":"2026-07-03T01:17:57.167127+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4P2TKU4ROJW","created_at":"2026-07-03T01:17:57.167127+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4P2TKU4ROJWM7QZ","created_at":"2026-07-03T01:17:57.167127+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4P2TKU4","created_at":"2026-07-03T01:17:57.167127+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/A4P2TKU4ROJWM7QZ2VPEQBNNSK","json":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK.json","graph_json":"https://pith.science/api/pith-number/A4P2TKU4ROJWM7QZ2VPEQBNNSK/graph.json","events_json":"https://pith.science/api/pith-number/A4P2TKU4ROJWM7QZ2VPEQBNNSK/events.json","paper":"https://pith.science/paper/A4P2TKU4"},"agent_actions":{"view_html":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK","download_json":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK.json","view_paper":"https://pith.science/paper/A4P2TKU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.02377&json=true","fetch_graph":"https://pith.science/api/pith-number/A4P2TKU4ROJWM7QZ2VPEQBNNSK/graph.json","fetch_events":"https://pith.science/api/pith-number/A4P2TKU4ROJWM7QZ2VPEQBNNSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK/action/storage_attestation","attest_author":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK/action/author_attestation","sign_citation":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK/action/citation_signature","submit_replication":"https://pith.science/pith/A4P2TKU4ROJWM7QZ2VPEQBNNSK/action/replication_record"}},"created_at":"2026-07-03T01:17:57.167127+00:00","updated_at":"2026-07-03T01:17:57.167127+00:00"}