{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FKDACGOKWIEUYWCKMEF5KLG625","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":"af4afcd8f8e716e2fbc46ce016d0adbb3b6fdc3713e6ac0a099ddda46d28b5d8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-30T04:46:05Z","title_canon_sha256":"9817e4f469dd22b7a414cedb2fa4118312c6668327712a41c4ceb91e32751eff"},"schema_version":"1.0","source":{"id":"2007.16029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.16029","created_at":"2026-07-05T01:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"2007.16029v2","created_at":"2026-07-05T01:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.16029","created_at":"2026-07-05T01:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"FKDACGOKWIEU","created_at":"2026-07-05T01:58:11Z"},{"alias_kind":"pith_short_16","alias_value":"FKDACGOKWIEUYWCK","created_at":"2026-07-05T01:58:11Z"},{"alias_kind":"pith_short_8","alias_value":"FKDACGOK","created_at":"2026-07-05T01:58:11Z"}],"graph_snapshots":[{"event_id":"sha256:a2d599f815badc3343af949134716058ca4ed996b9b19fd961f6f107d8e93c3f","target":"graph","created_at":"2026-07-05T01:58:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.16029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some asymptotic results, a few minimum distance bounds and further applications such as the trace representation and characterization of certain subfamilies of quasi-cyclic codes are elaborated. This survey will appear as a chapter in \"A Concise Encyclopedia of Coding Theory\" to be published by CRC Press.","authors_text":"Buket \\\"Ozkaya, Cem G\\\"uneri, San Ling","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-30T04:46:05Z","title":"Quasi-Cyclic Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.16029","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":"sha256:9233029428abf3ff9148999eba150322b0e04a263ac8ea7ccdf12ff5ec1fbf53","target":"record","created_at":"2026-07-05T01:58:11Z","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":"af4afcd8f8e716e2fbc46ce016d0adbb3b6fdc3713e6ac0a099ddda46d28b5d8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-30T04:46:05Z","title_canon_sha256":"9817e4f469dd22b7a414cedb2fa4118312c6668327712a41c4ceb91e32751eff"},"schema_version":"1.0","source":{"id":"2007.16029","kind":"arxiv","version":2}},"canonical_sha256":"2a860119cab2094c584a610bd52cded75fd4568aa1b3f119f8f3082733876add","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a860119cab2094c584a610bd52cded75fd4568aa1b3f119f8f3082733876add","first_computed_at":"2026-07-05T01:58:11.123134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:58:11.123134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gw8FYgilRz3VxKYTfIe+wH1Iv4X/916/DsvvXfFPwxqsFqma6nvcRtq0lzPyIbQJyB0utgEcQydXjptdpnT7DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:58:11.123606Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.16029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9233029428abf3ff9148999eba150322b0e04a263ac8ea7ccdf12ff5ec1fbf53","sha256:a2d599f815badc3343af949134716058ca4ed996b9b19fd961f6f107d8e93c3f"],"state_sha256":"f4eee684474ac6b41270e0257ed35ba3a3f296e94f362bb1860f3576ecb766ef"}