{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JEPNXIPJOHL6HZ2E4FDOVH3CG4","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":"5ed69329a4f4b1168a3fa2a972aa50c0a81f3ea35c0da53675c43793e2c83701","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-07T08:19:44Z","title_canon_sha256":"96aad3d1c12c95ad4452677576e08ed98b2271d5975fb6ca9c00ca66720457c5"},"schema_version":"1.0","source":{"id":"1009.1225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1225","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1225v1","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1225","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"JEPNXIPJOHL6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JEPNXIPJOHL6HZ2E","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JEPNXIPJ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:45bc74e973a384d71ec554ed09c996e3ec0cb7dfb6473ef5536ecf8efa765a29","target":"graph","created_at":"2026-05-18T04:41:15Z","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 $q$ be any prime power and let $d$ be a positive integer greater than 1. In this paper, we construct a family of $M$-ary sequences of period $q-1$ from a given $M$-ary, with $M|q-1$, Sidelikov sequence of period $q^d-1$. Under mild restrictions on $d$, we show that the maximum correlation magnitude of the family is upper bounded by $(2d -1) \\sqrt { q }+1$ and the asymptotic size, as $q\\rightarrow \\infty$, of that is $\\frac{ (M-1)q^{d-1}}{d }$. This extends the pioneering work of Yu and Gong for $d=2$ case.","authors_text":"Dae San Kim","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-07T08:19:44Z","title":"A family of sequences with large size and good correlation property arising from $M$-ary Sidelnikov sequences of period $q^d-1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1225","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:adc787c6d879547696b4e726b5b02066c4c581513107e05b7fdceac3c3c5441c","target":"record","created_at":"2026-05-18T04:41:15Z","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":"5ed69329a4f4b1168a3fa2a972aa50c0a81f3ea35c0da53675c43793e2c83701","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-07T08:19:44Z","title_canon_sha256":"96aad3d1c12c95ad4452677576e08ed98b2271d5975fb6ca9c00ca66720457c5"},"schema_version":"1.0","source":{"id":"1009.1225","kind":"arxiv","version":1}},"canonical_sha256":"491edba1e971d7e3e744e146ea9f623713ba8f61512fac5b6e2fa6407ea2db72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"491edba1e971d7e3e744e146ea9f623713ba8f61512fac5b6e2fa6407ea2db72","first_computed_at":"2026-05-18T04:41:15.916089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:15.916089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqZJxqdeHLs1EwELASAWrfFLkir6Osa/U3iUVzPwsI+ZiRMpXmOAF9DQ2r803ikRzGKp5f6ZxVH1vcIPNNisBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:15.916726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc787c6d879547696b4e726b5b02066c4c581513107e05b7fdceac3c3c5441c","sha256:45bc74e973a384d71ec554ed09c996e3ec0cb7dfb6473ef5536ecf8efa765a29"],"state_sha256":"585c7ee700a9057cf7520500febe9b8b0b25e018ef2d179d0edb6a977b66b3a3"}