{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2RPZLJVHMF43HDQ6GZTKVS3JMW","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":"97242551e57ae32087eb4daeb587b7da142b58ec9c5d51d50aa2c74db0bdab17","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T01:33:06Z","title_canon_sha256":"151735777e3b7ed762bba1ec1fb70384f120357dbd6fb48e75e37eb278603787"},"schema_version":"1.0","source":{"id":"1705.03982","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03982","created_at":"2026-05-18T00:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03982v2","created_at":"2026-05-18T00:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03982","created_at":"2026-05-18T00:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"2RPZLJVHMF43","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2RPZLJVHMF43HDQ6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2RPZLJVH","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:4ee4970b0294f1791bb26020232ad88a24d3acd060c551fd5b473c321ea19550","target":"graph","created_at":"2026-05-18T00:43:46Z","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":"Basic properties of a characteristic matrix for a tail-biting convolutional code are investigated. A tail-biting convolutional code can be regarded as a linear block code. Since the corresponding scalar generator matrix Gt has a kind of cyclic structure, an associated characteristic matrix also has a cyclic structure, from which basic properties of a characteristic matrix are obtained. Next, using the derived results, we discuss the possibility of trellis reduction for a given tail-biting convolutional code. There are cases where we can find a scalar generator matrix Gs equivalent to Gt based ","authors_text":"Masato Tajima","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T01:33:06Z","title":"Characteristic Matrices and Trellis Reduction for Tail-Biting Convolutional Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03982","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:acb7c6e03a1a5d5385bbeb75ecbba3a8375d698583f7c972d78b906867580c7f","target":"record","created_at":"2026-05-18T00:43:46Z","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":"97242551e57ae32087eb4daeb587b7da142b58ec9c5d51d50aa2c74db0bdab17","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T01:33:06Z","title_canon_sha256":"151735777e3b7ed762bba1ec1fb70384f120357dbd6fb48e75e37eb278603787"},"schema_version":"1.0","source":{"id":"1705.03982","kind":"arxiv","version":2}},"canonical_sha256":"d45f95a6a76179b38e1e3666aacb6965b8f30e2df921bac05ead3666f59cc0cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d45f95a6a76179b38e1e3666aacb6965b8f30e2df921bac05ead3666f59cc0cd","first_computed_at":"2026-05-18T00:43:46.088987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:46.088987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2vvnFibweveNcXHP7LXVFvrwsnRu/vB3GC5HZdS1+kxGHek7eNtT1lOwLFb2GpZkd+7ga3sbOS/4IsyI4ifCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:46.089477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03982","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acb7c6e03a1a5d5385bbeb75ecbba3a8375d698583f7c972d78b906867580c7f","sha256:4ee4970b0294f1791bb26020232ad88a24d3acd060c551fd5b473c321ea19550"],"state_sha256":"7f5529442c55bd1c9b326d7a9d232c47e0c555c4ccc183fc0e73cec09bbd7a75"}