{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7MNRL27S7YHYFZIALGOIADSNRP","short_pith_number":"pith:7MNRL27S","schema_version":"1.0","canonical_sha256":"fb1b15ebf2fe0f82e500599c800e4d8bdee3fb996883e8e765a7885709f399af","source":{"kind":"arxiv","id":"2501.03016","version":3},"attestation_state":"computed","paper":{"title":"Classification of LCD and self-dual codes over a finite non-unital local ring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anup Kushwaha, Indibar Debnath, Om Prakash, Patrick Sol\\'e","submitted_at":"2025-01-06T13:48:21Z","abstract_excerpt":"This work explores LCD and self-dual codes over a noncommutative non-unital ring $ E_p= \\langle r,s ~|~ pr =ps=0,~ r^2=r,~ s^2=s,~ rs=r,~ sr=s \\rangle$ of order $p^2$ where $p$ is a prime. Initially, we study the monomial equivalence of two free $E_p$-linear codes. In addition, a necessary and sufficient condition is derived for a free $E_p$-linear code to be MDS and almost MDS (shortly AMDS). Then, we use these results to classify MDS and AMDS LCD codes over $E_2$ and $E_3$ under monomial equivalence for lengths up to $6$. Subsequently, we study left self-dual codes over the ring $E_p$ and cl"},"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":"2501.03016","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-01-06T13:48:21Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bf7de04bc921132d3819507bd3a59946a5cbd93c2f13ba75712369150930916a","abstract_canon_sha256":"79ec7c905eb83cb19ca856c05b22ed10a36f30fddfd973dce9b1991937d99c8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:17:43.752517Z","signature_b64":"Z3rr3Z2dTNlb6oqRbPHgGI5qVDNRmidhJBynUT3uojtqyBSZdYQYKzn/Z1H1Ycm0TvcxnJvCRGoCigENL9t8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1b15ebf2fe0f82e500599c800e4d8bdee3fb996883e8e765a7885709f399af","last_reissued_at":"2026-06-25T01:17:43.752026Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:17:43.752026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of LCD and self-dual codes over a finite non-unital local ring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anup Kushwaha, Indibar Debnath, Om Prakash, Patrick Sol\\'e","submitted_at":"2025-01-06T13:48:21Z","abstract_excerpt":"This work explores LCD and self-dual codes over a noncommutative non-unital ring $ E_p= \\langle r,s ~|~ pr =ps=0,~ r^2=r,~ s^2=s,~ rs=r,~ sr=s \\rangle$ of order $p^2$ where $p$ is a prime. Initially, we study the monomial equivalence of two free $E_p$-linear codes. In addition, a necessary and sufficient condition is derived for a free $E_p$-linear code to be MDS and almost MDS (shortly AMDS). Then, we use these results to classify MDS and AMDS LCD codes over $E_2$ and $E_3$ under monomial equivalence for lengths up to $6$. Subsequently, we study left self-dual codes over the ring $E_p$ and cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03016","kind":"arxiv","version":3},"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/2501.03016/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":"2501.03016","created_at":"2026-06-25T01:17:43.752084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03016v3","created_at":"2026-06-25T01:17:43.752084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03016","created_at":"2026-06-25T01:17:43.752084+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MNRL27S7YHY","created_at":"2026-06-25T01:17:43.752084+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MNRL27S7YHYFZIA","created_at":"2026-06-25T01:17:43.752084+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MNRL27S","created_at":"2026-06-25T01:17:43.752084+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/7MNRL27S7YHYFZIALGOIADSNRP","json":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP.json","graph_json":"https://pith.science/api/pith-number/7MNRL27S7YHYFZIALGOIADSNRP/graph.json","events_json":"https://pith.science/api/pith-number/7MNRL27S7YHYFZIALGOIADSNRP/events.json","paper":"https://pith.science/paper/7MNRL27S"},"agent_actions":{"view_html":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP","download_json":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP.json","view_paper":"https://pith.science/paper/7MNRL27S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03016&json=true","fetch_graph":"https://pith.science/api/pith-number/7MNRL27S7YHYFZIALGOIADSNRP/graph.json","fetch_events":"https://pith.science/api/pith-number/7MNRL27S7YHYFZIALGOIADSNRP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP/action/storage_attestation","attest_author":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP/action/author_attestation","sign_citation":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP/action/citation_signature","submit_replication":"https://pith.science/pith/7MNRL27S7YHYFZIALGOIADSNRP/action/replication_record"}},"created_at":"2026-06-25T01:17:43.752084+00:00","updated_at":"2026-06-25T01:17:43.752084+00:00"}