{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:2UXF7GZH7UOKSRQHKZ2UIKOWE3","short_pith_number":"pith:2UXF7GZH","schema_version":"1.0","canonical_sha256":"d52e5f9b27fd1ca9460756754429d626e3bd92d30f56b9368b388426dc353684","source":{"kind":"arxiv","id":"2007.13309","version":1},"attestation_state":"computed","paper":{"title":"Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\\frac{q^{2m}-1}{q+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Q. Wang, T. Yan, X. Li, X. Zhao","submitted_at":"2020-07-27T04:56:14Z","abstract_excerpt":"In this paper, we study a family of constacyclic BCH codes over $\\mathbb{F}_{q^2}$ of length $n=\\frac{q^{2m}-1}{q+1}$, where $q$ is a prime power, and $m\\geq2$ an even integer. The maximum design distance of narrow-sense Hermitian dual-containing constacyclic BCH codes of length $n$ is determined. Furthermore, the exact dimension of the constacyclic BCH codes with given design distance is computed. As a consequence, we are able to derive the parameters of quantum codes as a function of their design parameters of the associated constacyclic BCH codes. This improves the result by Yuan et al. (De"},"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":"2007.13309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-07-27T04:56:14Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2bcfcb55fc408c25fc10a358f9b14e290c3ed22b7db3ff8287833ea8d673768e","abstract_canon_sha256":"9e764b687163a58412bb6edc7b3dc715b68b64319f6be5803862c8fa603df7f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:23.147477Z","signature_b64":"aHLXUcIodHzaRRSRZ3RdzlquID8FD93BWCGREAOyfM3E3SztTzZ7M3hD/TdmKYJwJpBEB+GLMhq/tMcPQeggAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d52e5f9b27fd1ca9460756754429d626e3bd92d30f56b9368b388426dc353684","last_reissued_at":"2026-07-05T01:22:23.147038Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:23.147038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hermitian dual-containing constacyclic BCH codes and related quantum codes of length $\\frac{q^{2m}-1}{q+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Q. Wang, T. Yan, X. Li, X. Zhao","submitted_at":"2020-07-27T04:56:14Z","abstract_excerpt":"In this paper, we study a family of constacyclic BCH codes over $\\mathbb{F}_{q^2}$ of length $n=\\frac{q^{2m}-1}{q+1}$, where $q$ is a prime power, and $m\\geq2$ an even integer. The maximum design distance of narrow-sense Hermitian dual-containing constacyclic BCH codes of length $n$ is determined. Furthermore, the exact dimension of the constacyclic BCH codes with given design distance is computed. As a consequence, we are able to derive the parameters of quantum codes as a function of their design parameters of the associated constacyclic BCH codes. This improves the result by Yuan et al. (De"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13309","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.13309/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2007.13309","created_at":"2026-07-05T01:22:23.147113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.13309v1","created_at":"2026-07-05T01:22:23.147113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13309","created_at":"2026-07-05T01:22:23.147113+00:00"},{"alias_kind":"pith_short_12","alias_value":"2UXF7GZH7UOK","created_at":"2026-07-05T01:22:23.147113+00:00"},{"alias_kind":"pith_short_16","alias_value":"2UXF7GZH7UOKSRQH","created_at":"2026-07-05T01:22:23.147113+00:00"},{"alias_kind":"pith_short_8","alias_value":"2UXF7GZH","created_at":"2026-07-05T01:22:23.147113+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/2UXF7GZH7UOKSRQHKZ2UIKOWE3","json":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3.json","graph_json":"https://pith.science/api/pith-number/2UXF7GZH7UOKSRQHKZ2UIKOWE3/graph.json","events_json":"https://pith.science/api/pith-number/2UXF7GZH7UOKSRQHKZ2UIKOWE3/events.json","paper":"https://pith.science/paper/2UXF7GZH"},"agent_actions":{"view_html":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3","download_json":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3.json","view_paper":"https://pith.science/paper/2UXF7GZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.13309&json=true","fetch_graph":"https://pith.science/api/pith-number/2UXF7GZH7UOKSRQHKZ2UIKOWE3/graph.json","fetch_events":"https://pith.science/api/pith-number/2UXF7GZH7UOKSRQHKZ2UIKOWE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3/action/storage_attestation","attest_author":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3/action/author_attestation","sign_citation":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3/action/citation_signature","submit_replication":"https://pith.science/pith/2UXF7GZH7UOKSRQHKZ2UIKOWE3/action/replication_record"}},"created_at":"2026-07-05T01:22:23.147113+00:00","updated_at":"2026-07-05T01:22:23.147113+00:00"}