{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NQL66SPA3MFJN2S6EWJSMYIXTW","short_pith_number":"pith:NQL66SPA","schema_version":"1.0","canonical_sha256":"6c17ef49e0db0a96ea5e25932661179d8a88ff2a598fe3d07f7da26531f2553c","source":{"kind":"arxiv","id":"1506.02820","version":1},"attestation_state":"computed","paper":{"title":"Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DM","math.CO","math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Alexander Zeh, Markus Ulmschneider","submitted_at":"2015-06-09T08:27:08Z","abstract_excerpt":"The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time prob"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.02820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-09T08:27:08Z","cross_cats_sorted":["cs.CR","cs.DM","math.CO","math.IT","math.NT"],"title_canon_sha256":"944be9b4d747545444e3271b07a7a190d0b6d1574a47908b92e9d4ded7ba4815","abstract_canon_sha256":"d8c3a7b6f1fd55942b91e0fa18743625dcf6d77e281f47d632a6b12bce1618a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:40.826027Z","signature_b64":"b73swiiNcd7+emVKLZhu633M/mZacwY/M8G1uyigbJo33PiOr0ZmbZ3WGZ4o/UTZrO5eiMs2JEyUeZ5WYLKBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c17ef49e0db0a96ea5e25932661179d8a88ff2a598fe3d07f7da26531f2553c","last_reissued_at":"2026-05-18T01:55:40.825386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:40.825386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DM","math.CO","math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Alexander Zeh, Markus Ulmschneider","submitted_at":"2015-06-09T08:27:08Z","abstract_excerpt":"The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We generalize these two bounds to the case of repeated-root cyclic codes and present a syndrome-based burst error decoding algorithm with guaranteed decoding radius based on an associated folded cyclic code. Furthermore, we present a third technique for bounding the minimum Hamming distance based on the embedding of a given repeated-root cyclic code into a repeated-root cyclic product code. A second quadratic-time prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02820","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.02820","created_at":"2026-05-18T01:55:40.825486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02820v1","created_at":"2026-05-18T01:55:40.825486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02820","created_at":"2026-05-18T01:55:40.825486+00:00"},{"alias_kind":"pith_short_12","alias_value":"NQL66SPA3MFJ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NQL66SPA3MFJN2S6","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NQL66SPA","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW","json":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW.json","graph_json":"https://pith.science/api/pith-number/NQL66SPA3MFJN2S6EWJSMYIXTW/graph.json","events_json":"https://pith.science/api/pith-number/NQL66SPA3MFJN2S6EWJSMYIXTW/events.json","paper":"https://pith.science/paper/NQL66SPA"},"agent_actions":{"view_html":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW","download_json":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW.json","view_paper":"https://pith.science/paper/NQL66SPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02820&json=true","fetch_graph":"https://pith.science/api/pith-number/NQL66SPA3MFJN2S6EWJSMYIXTW/graph.json","fetch_events":"https://pith.science/api/pith-number/NQL66SPA3MFJN2S6EWJSMYIXTW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW/action/storage_attestation","attest_author":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW/action/author_attestation","sign_citation":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW/action/citation_signature","submit_replication":"https://pith.science/pith/NQL66SPA3MFJN2S6EWJSMYIXTW/action/replication_record"}},"created_at":"2026-05-18T01:55:40.825486+00:00","updated_at":"2026-05-18T01:55:40.825486+00:00"}