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Indeed, first for all integers $k$, we determine exact values of the $k$-error linear complexity over the finite field $\\F_2$ for these binary sequences under the assumption of  f2 being a primitive root modulo $p^2$, and then we determine their $k$-error linear compl"},"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":"1307.6626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-07-25T03:28:42Z","cross_cats_sorted":[],"title_canon_sha256":"00b47d22aa1676cdac90c400ac7791fd3dae12a4deb06e4e272fe5ec625e4e7c","abstract_canon_sha256":"a60734a2905cdc8a2bd5b3184949b45fe5d671cb2d13461eaa602275c7c8c20b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:14.519559Z","signature_b64":"VbvkVF4RU5t3BGCkC9b2L5VkZzUG5YQp/i5PawGP1bclmbBkFBJrLGT+P13Q4IEyNaSz0YbGCkEg/pNs2hmGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96ea567599b88b3c656058bf0a9718a7e36f7beedf698124e60c468f0fa91d75","last_reissued_at":"2026-05-18T01:19:14.518780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:14.518780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $k$-error linear complexity of binary sequences derived from polynomial quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Chenhuang Wu, Zhihua Niu, Zhixiong Chen","submitted_at":"2013-07-25T03:28:42Z","abstract_excerpt":"We investigate the $k$-error linear complexity of $p^2$-periodic binary sequences defined from the polynomial quotients (including the well-studied Fermat quotients), which is defined by $$ q_{p,w}(u)\\equiv \\frac{u^w-u^{wp}}{p} \\bmod p ~ \\mathrm{with} 0 \\le q_{p,w}(u) \\le p-1, ~u\\ge 0, $$ where $p$ is an odd prime and $1\\le w<p$. Indeed, first for all integers $k$, we determine exact values of the $k$-error linear complexity over the finite field $\\F_2$ for these binary sequences under the assumption of  f2 being a primitive root modulo $p^2$, and then we determine their $k$-error linear compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6626","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":"1307.6626","created_at":"2026-05-18T01:19:14.518913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.6626v1","created_at":"2026-05-18T01:19:14.518913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6626","created_at":"2026-05-18T01:19:14.518913+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3VFM5MZXCFT","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3VFM5MZXCFTYZLA","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3VFM5MZ","created_at":"2026-05-18T12:27:59.945178+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/S3VFM5MZXCFTYZLALC7QVFYYU7","json":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7.json","graph_json":"https://pith.science/api/pith-number/S3VFM5MZXCFTYZLALC7QVFYYU7/graph.json","events_json":"https://pith.science/api/pith-number/S3VFM5MZXCFTYZLALC7QVFYYU7/events.json","paper":"https://pith.science/paper/S3VFM5MZ"},"agent_actions":{"view_html":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7","download_json":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7.json","view_paper":"https://pith.science/paper/S3VFM5MZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.6626&json=true","fetch_graph":"https://pith.science/api/pith-number/S3VFM5MZXCFTYZLALC7QVFYYU7/graph.json","fetch_events":"https://pith.science/api/pith-number/S3VFM5MZXCFTYZLALC7QVFYYU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7/action/storage_attestation","attest_author":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7/action/author_attestation","sign_citation":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7/action/citation_signature","submit_replication":"https://pith.science/pith/S3VFM5MZXCFTYZLALC7QVFYYU7/action/replication_record"}},"created_at":"2026-05-18T01:19:14.518913+00:00","updated_at":"2026-05-18T01:19:14.518913+00:00"}