{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:K2IHVE7W4GQAPS7ASZE7BG7K3W","short_pith_number":"pith:K2IHVE7W","canonical_record":{"source":{"id":"1811.11018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-27T14:27:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ac5d6dfb696eab2a4a847af084d8313207d7c5eaf666b773fea49585a90e06da","abstract_canon_sha256":"3c0519bad635198d75815e604c7a27ebac749ad45e0601dac918458bcba97081"},"schema_version":"1.0"},"canonical_sha256":"56907a93f6e1a007cbe09649f09beadd8eca61ec5637f0e61d0f9deb183e5354","source":{"kind":"arxiv","id":"1811.11018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11018","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11018v1","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11018","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"K2IHVE7W4GQA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K2IHVE7W4GQAPS7A","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K2IHVE7W","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:K2IHVE7W4GQAPS7ASZE7BG7K3W","target":"record","payload":{"canonical_record":{"source":{"id":"1811.11018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-27T14:27:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ac5d6dfb696eab2a4a847af084d8313207d7c5eaf666b773fea49585a90e06da","abstract_canon_sha256":"3c0519bad635198d75815e604c7a27ebac749ad45e0601dac918458bcba97081"},"schema_version":"1.0"},"canonical_sha256":"56907a93f6e1a007cbe09649f09beadd8eca61ec5637f0e61d0f9deb183e5354","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:45.472641Z","signature_b64":"svWFUwtFA9yaL2gNF2gKkiEiRfFhFaNtcQai6i1JwhCfSYP8y5iTbzi86A9rOP7rkrtIxNGpr9VdYRZ5ri6UAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56907a93f6e1a007cbe09649f09beadd8eca61ec5637f0e61d0f9deb183e5354","last_reissued_at":"2026-05-17T23:59:45.472245Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:45.472245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.11018","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4CfKJp45tmdW/hzmQEGaUD63Np6S4zCfkBn7il2vL+YxmxVneAzgyprSEBYaqJAR7Qwz+l+bM5zoOca8Pnr/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:29:42.680691Z"},"content_sha256":"caca97d794e4ec00727a808cbc8e96372e946abc354ad8a9345a02fce76018e1","schema_version":"1.0","event_id":"sha256:caca97d794e4ec00727a808cbc8e96372e946abc354ad8a9345a02fce76018e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:K2IHVE7W4GQAPS7ASZE7BG7K3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit representation and enumeration for self-dual cyclic codes over $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ of length $2^s$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hai Q. Dinh, Somphong Jitman, Yonglin Cao, Yuan Cao","submitted_at":"2018-11-27T14:27:35Z","abstract_excerpt":"Let $\\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over $\\mathbb{F}_{2^m}$, an efficient method for the construction of all distinct self-dual cyclic codes with length $2^s$ over the finite chain ring $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ $(u^2=0)$ is provided. On that basis, an explicit representation for every self-dual cyclic code of length $2^s$ over $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ and an exact formula to count the number of all these self-dual cyclic codes are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11018","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"guoexligY9ItLSqpIUoYygPAtjLbKr0Nn3oTE62JeY5eB25o7SJvoHFcbaJFWbp7oG78XFCTFoFdfGcjaIbeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:29:42.681025Z"},"content_sha256":"58aa40a538625bdc82ced1b3a8f04edc9181becd0d468058f6b4671915c0719b","schema_version":"1.0","event_id":"sha256:58aa40a538625bdc82ced1b3a8f04edc9181becd0d468058f6b4671915c0719b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/bundle.json","state_url":"https://pith.science/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T16:29:42Z","links":{"resolver":"https://pith.science/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W","bundle":"https://pith.science/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/bundle.json","state":"https://pith.science/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2IHVE7W4GQAPS7ASZE7BG7K3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K2IHVE7W4GQAPS7ASZE7BG7K3W","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":"3c0519bad635198d75815e604c7a27ebac749ad45e0601dac918458bcba97081","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-27T14:27:35Z","title_canon_sha256":"ac5d6dfb696eab2a4a847af084d8313207d7c5eaf666b773fea49585a90e06da"},"schema_version":"1.0","source":{"id":"1811.11018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.11018","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"1811.11018v1","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.11018","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"K2IHVE7W4GQA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K2IHVE7W4GQAPS7A","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K2IHVE7W","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:58aa40a538625bdc82ced1b3a8f04edc9181becd0d468058f6b4671915c0719b","target":"graph","created_at":"2026-05-17T23:59:45Z","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":"Let $\\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over $\\mathbb{F}_{2^m}$, an efficient method for the construction of all distinct self-dual cyclic codes with length $2^s$ over the finite chain ring $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ $(u^2=0)$ is provided. On that basis, an explicit representation for every self-dual cyclic code of length $2^s$ over $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ and an exact formula to count the number of all these self-dual cyclic codes are","authors_text":"Hai Q. Dinh, Somphong Jitman, Yonglin Cao, Yuan Cao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-27T14:27:35Z","title":"An explicit representation and enumeration for self-dual cyclic codes over $\\mathbb{F}_{2^m}+u\\mathbb{F}_{2^m}$ of length $2^s$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11018","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:caca97d794e4ec00727a808cbc8e96372e946abc354ad8a9345a02fce76018e1","target":"record","created_at":"2026-05-17T23:59:45Z","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":"3c0519bad635198d75815e604c7a27ebac749ad45e0601dac918458bcba97081","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-11-27T14:27:35Z","title_canon_sha256":"ac5d6dfb696eab2a4a847af084d8313207d7c5eaf666b773fea49585a90e06da"},"schema_version":"1.0","source":{"id":"1811.11018","kind":"arxiv","version":1}},"canonical_sha256":"56907a93f6e1a007cbe09649f09beadd8eca61ec5637f0e61d0f9deb183e5354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56907a93f6e1a007cbe09649f09beadd8eca61ec5637f0e61d0f9deb183e5354","first_computed_at":"2026-05-17T23:59:45.472245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:45.472245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svWFUwtFA9yaL2gNF2gKkiEiRfFhFaNtcQai6i1JwhCfSYP8y5iTbzi86A9rOP7rkrtIxNGpr9VdYRZ5ri6UAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:45.472641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.11018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caca97d794e4ec00727a808cbc8e96372e946abc354ad8a9345a02fce76018e1","sha256:58aa40a538625bdc82ced1b3a8f04edc9181becd0d468058f6b4671915c0719b"],"state_sha256":"c2cc4d3d5847c525c5acc23992e6b41702f9ef6f6ee782db78f2a69946ae6a0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jzc4RGJoDZfmoMC16ShMLZUQDHS6RDgJ+7CQ8CsAjyQq/UbASe6JdqTJ2hFcgJMyMg0n6C+Lf6A+7FqRpB6hCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:29:42.682836Z","bundle_sha256":"98c28681983a9444e239556c6d884effc99359e083303887b5180bbbb253e2a2"}}