{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S34EGMPB2SFI2XDTZBBRZKJBVF","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":"d34ae8bcb9e241642f6692c0b610fc6320f527511f7e7d4d175d31ea11977968","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-18T11:01:53Z","title_canon_sha256":"9d4245e284935bdfce4cdc1f9de6913aa6269794530b22dcbefa8de76c3e88ae"},"schema_version":"1.0","source":{"id":"1601.04467","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04467","created_at":"2026-05-18T00:54:08Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04467v2","created_at":"2026-05-18T00:54:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04467","created_at":"2026-05-18T00:54:08Z"},{"alias_kind":"pith_short_12","alias_value":"S34EGMPB2SFI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S34EGMPB2SFI2XDT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S34EGMPB","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:9163a09be734097114d15ddb99fdea7c451b52cb705ee92872e26b32d8b2e332","target":"graph","created_at":"2026-05-18T00:54:08Z","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":"Both MDS and Euclidean self-dual codes have theoretical and practical importance and the study of MDS self-dual codes has attracted lots of attention in recent years. In particular, determining existence of $q$-ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. The current paper focuses on the case where $q$ is odd. We construct a few classes of new MDS self-dual code through generalized Reed-Solomon codes. More precisely, we show that for any given even length $n$ we have a $q$-ary MDS code as long as","authors_text":"Chaoping Xing, Lingfei Jin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-18T11:01:53Z","title":"New MDS Self-Dual Codes from Generalized Reed-Solomon Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04467","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:f9795d19c2befdf1bb2dcfb3c566b388c3d922c0ad00ff3429e4cf69dbdf23a6","target":"record","created_at":"2026-05-18T00:54:08Z","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":"d34ae8bcb9e241642f6692c0b610fc6320f527511f7e7d4d175d31ea11977968","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-18T11:01:53Z","title_canon_sha256":"9d4245e284935bdfce4cdc1f9de6913aa6269794530b22dcbefa8de76c3e88ae"},"schema_version":"1.0","source":{"id":"1601.04467","kind":"arxiv","version":2}},"canonical_sha256":"96f84331e1d48a8d5c73c8431ca921a94aebbd821e21e12a7e0f95961a0e9ba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96f84331e1d48a8d5c73c8431ca921a94aebbd821e21e12a7e0f95961a0e9ba2","first_computed_at":"2026-05-18T00:54:08.998266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:08.998266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+KZKpLIrczisXGRgl0GZAL5Ijja4jYShetLLaLDeIFDQEfZpNbxLKSn0qtqJsoStjotaPalvmDjGFTne2APqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:08.998664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04467","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9795d19c2befdf1bb2dcfb3c566b388c3d922c0ad00ff3429e4cf69dbdf23a6","sha256:9163a09be734097114d15ddb99fdea7c451b52cb705ee92872e26b32d8b2e332"],"state_sha256":"b1c75849061ed24cd0ba5626626995e7e7b4b493f1c98fa9d79995b0740127ee"}