{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YXOF6G4K5FNDPNNWCGIOZRL3UR","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":"a47dbc53c110918ad74201ad3340dbdec4dec97958f26d278427cf73c3d986da","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-16T06:15:22Z","title_canon_sha256":"ff018489135ef17227dacf80239051c1555c3a75b4a6b3b1bb06a09e7c98fdd5"},"schema_version":"1.0","source":{"id":"1701.04180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04180","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04180v1","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04180","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"YXOF6G4K5FND","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXOF6G4K5FNDPNNW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXOF6G4K","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d65fcaa8ad6d68666fbe72d2b59300845198aabcacfba7f52b0f280850ac36b4","target":"graph","created_at":"2026-05-18T00:52:47Z","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":"As far as we know, there is no decoding algorithm of any binary self-dual $[40, 20, 8]$ code except for the syndrome decoding applied to the code directly. This syndrome decoding for a binary self-dual $[40,20,8]$ code is not efficient in the sense that it cannot be done by hand due to a large syndrome table. The purpose of this paper is to give two new efficient decoding algorithms for an extremal binary doubly-even self-dual $[40,20, 8]$ code $C_{40,1}^{DE}$ by hand with the help of a Hermitian self-dual $[10,5,4]$ code $E_{10}$ over $GF(4)$. The main idea of this decoding is to project code","authors_text":"Jon-Lark Kim, Nari Lee","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-16T06:15:22Z","title":"A Projection Decoding of a Binary Extremal Self-Dual Code of Length $40$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04180","kind":"arxiv","version":1},"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:f5d090ceb838cc94a5a89cdab474c3d92196c6e374c95a159f1e794cf9101637","target":"record","created_at":"2026-05-18T00:52:47Z","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":"a47dbc53c110918ad74201ad3340dbdec4dec97958f26d278427cf73c3d986da","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-16T06:15:22Z","title_canon_sha256":"ff018489135ef17227dacf80239051c1555c3a75b4a6b3b1bb06a09e7c98fdd5"},"schema_version":"1.0","source":{"id":"1701.04180","kind":"arxiv","version":1}},"canonical_sha256":"c5dc5f1b8ae95a37b5b61190ecc57ba4667e549d6bc5c5b35a488ccd53f17b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5dc5f1b8ae95a37b5b61190ecc57ba4667e549d6bc5c5b35a488ccd53f17b9c","first_computed_at":"2026-05-18T00:52:47.591286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:47.591286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TbigsIAi+CEW8EqGtzxBsPm3q0TzDR5OwEOmkVKrgptNRSG/eYNQTRsauiZYS9onJolfGeUQ0s7Hei8AVD1bCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:47.592030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5d090ceb838cc94a5a89cdab474c3d92196c6e374c95a159f1e794cf9101637","sha256:d65fcaa8ad6d68666fbe72d2b59300845198aabcacfba7f52b0f280850ac36b4"],"state_sha256":"518630e93d448d50863cd2e645a7e5e859cffd7f0a7006e41404944384ed3f38"}