{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4FLFKF2ZXUJWX5666DFSHSATH2","short_pith_number":"pith:4FLFKF2Z","schema_version":"1.0","canonical_sha256":"e156551759bd136bf7def0cb23c8133eadfafcf7b4a2ec81fa2b61a3f1dce6d6","source":{"kind":"arxiv","id":"2208.13389","version":3},"attestation_state":"computed","paper":{"title":"Several classes of Galois self-orthogonal MDS codes and related applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Shitao Li, Shixin Zhu, Yang Li, Yunfei Su","submitted_at":"2022-08-29T06:42:33Z","abstract_excerpt":"Let $q=p^h$ be a prime power and $e$ be an integer with $0\\leq e\\leq h-1$. $e$-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes ($e=0$) and Hermitian self-orthogonal codes ($e=\\frac{h}{2}$ and $h$ is even). In this paper, we propose two general methods to construct $e$-Galois self-orthogonal (extended) generalized Reed-Solomon (GRS) codes. As a consequence, eight new classes of $e$-Galois self-orthogonal (extended) GRS codes with odd $q$ and $2e\\mid h$ are obtained. Based on the Galois dual of a code, we also study its punctured and shortened codes. As applic"},"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":"2208.13389","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-08-29T06:42:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"15964cfb573cf1e6142ced1772384ada1bb3803e56524cf5dee191fdba0e7531","abstract_canon_sha256":"295ac428e0eb1f0a278cf1c7b9fd653eb52f52164fd3f962e83b22b068b6fdf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:40:08.384664Z","signature_b64":"ek6dJFy6EDJ0iOp3wvg7Ex37ipjA1kBAfwSD50/RkESCs5DxlPo63vcDJNyi8afRGduJW8eH1VnNwH3DJWpfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e156551759bd136bf7def0cb23c8133eadfafcf7b4a2ec81fa2b61a3f1dce6d6","last_reissued_at":"2026-07-05T05:40:08.384192Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:40:08.384192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Several classes of Galois self-orthogonal MDS codes and related applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Shitao Li, Shixin Zhu, Yang Li, Yunfei Su","submitted_at":"2022-08-29T06:42:33Z","abstract_excerpt":"Let $q=p^h$ be a prime power and $e$ be an integer with $0\\leq e\\leq h-1$. $e$-Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes ($e=0$) and Hermitian self-orthogonal codes ($e=\\frac{h}{2}$ and $h$ is even). In this paper, we propose two general methods to construct $e$-Galois self-orthogonal (extended) generalized Reed-Solomon (GRS) codes. As a consequence, eight new classes of $e$-Galois self-orthogonal (extended) GRS codes with odd $q$ and $2e\\mid h$ are obtained. Based on the Galois dual of a code, we also study its punctured and shortened codes. As applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.13389","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/2208.13389/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":"2208.13389","created_at":"2026-07-05T05:40:08.384248+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.13389v3","created_at":"2026-07-05T05:40:08.384248+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.13389","created_at":"2026-07-05T05:40:08.384248+00:00"},{"alias_kind":"pith_short_12","alias_value":"4FLFKF2ZXUJW","created_at":"2026-07-05T05:40:08.384248+00:00"},{"alias_kind":"pith_short_16","alias_value":"4FLFKF2ZXUJWX566","created_at":"2026-07-05T05:40:08.384248+00:00"},{"alias_kind":"pith_short_8","alias_value":"4FLFKF2Z","created_at":"2026-07-05T05:40:08.384248+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/4FLFKF2ZXUJWX5666DFSHSATH2","json":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2.json","graph_json":"https://pith.science/api/pith-number/4FLFKF2ZXUJWX5666DFSHSATH2/graph.json","events_json":"https://pith.science/api/pith-number/4FLFKF2ZXUJWX5666DFSHSATH2/events.json","paper":"https://pith.science/paper/4FLFKF2Z"},"agent_actions":{"view_html":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2","download_json":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2.json","view_paper":"https://pith.science/paper/4FLFKF2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.13389&json=true","fetch_graph":"https://pith.science/api/pith-number/4FLFKF2ZXUJWX5666DFSHSATH2/graph.json","fetch_events":"https://pith.science/api/pith-number/4FLFKF2ZXUJWX5666DFSHSATH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2/action/storage_attestation","attest_author":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2/action/author_attestation","sign_citation":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2/action/citation_signature","submit_replication":"https://pith.science/pith/4FLFKF2ZXUJWX5666DFSHSATH2/action/replication_record"}},"created_at":"2026-07-05T05:40:08.384248+00:00","updated_at":"2026-07-05T05:40:08.384248+00:00"}